<p>The moduli space <span></span><math> <semantics> <mrow> <mi>Y</mi> <mo>=</mo> <mi>Y</mi> <mo>(</mo> <msub> <mi>E</mi> <mn>6</mn> </msub> <mo>)</mo> </mrow> <annotation>$Y = Y(E_6)$</annotation> </semantics></math> of marked cubic surfaces is one of the most classical moduli spaces in algebraic geometry, dating back to the nineteenth-century work of Cayley and Salmon. Modern interest in <span></span><math> <semantics> <mi>Y</mi> <annotation>$Y$</annotation> </semantics></math> was restored in the 1980s by Naruki's explicit construction of a <span></span><math> <semantics> <mrow> <mi>W</mi> <mo>(</mo> <msub> <mi>E</mi> <mn>6</mn> </msub> <mo>)</mo> </mrow> <annotation>$W(E_6)$</annotation> </semantics></math>-equivariant smooth projective compactification <span></span><math> <semantics> <mover> <mi>Y</mi> <mo>¯</mo> </mover> <annotation>${overline{Y}}$</annotation> </semantics></math> of <span></span><math> <semantics> <mi>Y</mi> <annotation>$Y$</annotation> </semantics></math>, and in the 2000s by Hacking, Keel, and Tevelev's construction of the Kollár–Shepherd-Barron–Alexeev (KSBA) stable pair compactification <span></span><math> <semantics> <mover> <mi>Y</mi> <mo>∼</mo> </mover> <annotation>${widetilde{Y}}$</annotation> </semantics></math> of <span></span><math> <semantics> <mi>Y</mi> <annotation>$Y$</annotation> </semantics></math> as a natural sequence of blowups of <span></span><math> <semantics> <mover> <mi>Y</mi> <mo>¯</mo> </mover> <annotation>${overline{Y}}$</annotation> </semantics></math>. We describe generators for the cones of <span></span><math> <semantics> <mrow> <mi>W</mi> <mo>(</mo> <msub> <mi>E</mi> <mn>6</mn> </msub> <mo>)</mo> </mrow> <
{"title":"The \u0000 \u0000 \u0000 W\u0000 (\u0000 \u0000 E\u0000 6\u0000 \u0000 )\u0000 \u0000 $W(E_6)$\u0000 -invariant birational geometry of the moduli space of marked cubic surfaces","authors":"Nolan Schock","doi":"10.1002/mana.202300459","DOIUrl":"10.1002/mana.202300459","url":null,"abstract":"<p>The moduli space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Y</mi>\u0000 <mo>=</mo>\u0000 <mi>Y</mi>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mn>6</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$Y = Y(E_6)$</annotation>\u0000 </semantics></math> of marked cubic surfaces is one of the most classical moduli spaces in algebraic geometry, dating back to the nineteenth-century work of Cayley and Salmon. Modern interest in <span></span><math>\u0000 <semantics>\u0000 <mi>Y</mi>\u0000 <annotation>$Y$</annotation>\u0000 </semantics></math> was restored in the 1980s by Naruki's explicit construction of a <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>W</mi>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mn>6</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$W(E_6)$</annotation>\u0000 </semantics></math>-equivariant smooth projective compactification <span></span><math>\u0000 <semantics>\u0000 <mover>\u0000 <mi>Y</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 <annotation>${overline{Y}}$</annotation>\u0000 </semantics></math> of <span></span><math>\u0000 <semantics>\u0000 <mi>Y</mi>\u0000 <annotation>$Y$</annotation>\u0000 </semantics></math>, and in the 2000s by Hacking, Keel, and Tevelev's construction of the Kollár–Shepherd-Barron–Alexeev (KSBA) stable pair compactification <span></span><math>\u0000 <semantics>\u0000 <mover>\u0000 <mi>Y</mi>\u0000 <mo>∼</mo>\u0000 </mover>\u0000 <annotation>${widetilde{Y}}$</annotation>\u0000 </semantics></math> of <span></span><math>\u0000 <semantics>\u0000 <mi>Y</mi>\u0000 <annotation>$Y$</annotation>\u0000 </semantics></math> as a natural sequence of blowups of <span></span><math>\u0000 <semantics>\u0000 <mover>\u0000 <mi>Y</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 <annotation>${overline{Y}}$</annotation>\u0000 </semantics></math>. We describe generators for the cones of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>W</mi>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mn>6</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 7","pages":"2639-2666"},"PeriodicalIF":0.8,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300459","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study families of analytic semigroups, acting on a Banach space, and depending on a parameter, and give sufficient conditions for existence of uniform with respect to the parameter norm bounds using spectral properties of the respective semigroup generators. In particular, we use estimates of the resolvent operators of the generators along vertical segments to estimate the growth/decay rate of the norm for the family of analytic semigroups. These results are applied to prove the Lyapunov linear stability of planar traveling waves of systems of reaction–diffusion equations, and the bidomain equation, important in electrophysiology.
{"title":"Uniform bounds of families of analytic semigroups and Lyapunov Linear Stability of planar fronts","authors":"Yuri Latushkin, Alin Pogan","doi":"10.1002/mana.202300273","DOIUrl":"10.1002/mana.202300273","url":null,"abstract":"<p>We study families of analytic semigroups, acting on a Banach space, and depending on a parameter, and give sufficient conditions for existence of uniform with respect to the parameter norm bounds using spectral properties of the respective semigroup generators. In particular, we use estimates of the resolvent operators of the generators along vertical segments to estimate the growth/decay rate of the norm for the family of analytic semigroups. These results are applied to prove the Lyapunov linear stability of planar traveling waves of systems of reaction–diffusion equations, and the bidomain equation, important in electrophysiology.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 7","pages":"2750-2785"},"PeriodicalIF":0.8,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The aim of this paper is to describe the equivariant and ordinary Grothendieck ring and the equivariant and ordinary topological -ring of flag Bott manifolds of the general Lie type. This will generalize the results on the equivariant and ordinary cohomology of flag Bott manifolds of the general Lie type due to Kaji, Kuroki, Lee, and Suh.
{"title":"Equivariant \u0000 \u0000 K\u0000 $K$\u0000 -theory of flag Bott manifolds of general Lie type","authors":"Bidhan Paul, Vikraman Uma","doi":"10.1002/mana.202300423","DOIUrl":"10.1002/mana.202300423","url":null,"abstract":"<p>The aim of this paper is to describe the equivariant and ordinary Grothendieck ring and the equivariant and ordinary topological <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>-ring of flag Bott manifolds of the general Lie type. This will generalize the results on the equivariant and ordinary cohomology of flag Bott manifolds of the general Lie type due to Kaji, Kuroki, Lee, and Suh.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 7","pages":"2786-2804"},"PeriodicalIF":0.8,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
<p>Koplienko [Sib. Mat. Zh. 25 (1984), 62–71; English transl. in Siberian Math. J. 25 (1984), 735–743] found a trace formula for perturbations of self-adjoint operators by operators of Hilbert–Schmidt class <span></span><math> <semantics> <mrow> <msub> <mi>B</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>H</mi> <mo>)</mo> </mrow> </mrow> <annotation>$mathcal {B}_2(mathcal {H})$</annotation> </semantics></math>. Later, Neidhardt introduced a similar formula in the case of pairs of unitaries <span></span><math> <semantics> <mrow> <mo>(</mo> <mi>U</mi> <mo>,</mo> <msub> <mi>U</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <annotation>$(U,U_0)$</annotation> </semantics></math> via multiplicative path in [Math. Nachr. 138 (1988), 7–25]. In 2012, Potapov and Sukochev [Comm. Math. Phys. 309 (2012), no. 3, 693–702] obtained a trace formula like the Koplienko trace formula for pairs of contractions by answering an open question posed by Gesztesy, Pushnitski, and Simon [Zh. Mat. Fiz. Anal. Geom. 4 (2008), no. 1, 63–107, 202; Open Question 11.2]. In this paper, we supply a new proof of the Koplienko trace formula in the case of pairs of contractions <span></span><math> <semantics> <mrow> <mo>(</mo> <mi>T</mi> <mo>,</mo> <msub> <mi>T</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <annotation>$(T,T_0)$</annotation> </semantics></math>, where the initial operator <span></span><math> <semantics> <msub> <mi>T</mi> <mn>0</mn> </msub> <annotation>$T_0$</annotation> </semantics></math> is normal, via linear path by reducing the problem to a finite-dimensional one as in the proof of Krein's trace formula by Voiculescu [Oper. Theory Adv. Appl. 24 (1987) 329–332] and Sinha and Mohapatra [Proc. Indian Acad. Sci. Math. Sci. 104 (1994), no. 4, 819–853] and [Integral Equations Operator Theory 24 (1996), no. 3, 285–297]. Consequently, we obtain the Koplienko trace formula for a class of pairs of contractions using the Schäffer matrix unitary dilation. Moreover, we also obtain the Koplienko trace formula for a pair of self-adjoint operators and maximal dissipative operators using the Cayley transform. At the end, we extend the Koplienko–Neidhardt trace formula for a class of pairs of contractions <span></span
{"title":"Second-order trace formulas","authors":"Arup Chattopadhyay, Soma Das, Chandan Pradhan","doi":"10.1002/mana.202200295","DOIUrl":"10.1002/mana.202200295","url":null,"abstract":"<p>Koplienko [Sib. Mat. Zh. 25 (1984), 62–71; English transl. in Siberian Math. J. 25 (1984), 735–743] found a trace formula for perturbations of self-adjoint operators by operators of Hilbert–Schmidt class <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>B</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>H</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathcal {B}_2(mathcal {H})$</annotation>\u0000 </semantics></math>. Later, Neidhardt introduced a similar formula in the case of pairs of unitaries <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>U</mi>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>U</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(U,U_0)$</annotation>\u0000 </semantics></math> via multiplicative path in [Math. Nachr. 138 (1988), 7–25]. In 2012, Potapov and Sukochev [Comm. Math. Phys. 309 (2012), no. 3, 693–702] obtained a trace formula like the Koplienko trace formula for pairs of contractions by answering an open question posed by Gesztesy, Pushnitski, and Simon [Zh. Mat. Fiz. Anal. Geom. 4 (2008), no. 1, 63–107, 202; Open Question 11.2]. In this paper, we supply a new proof of the Koplienko trace formula in the case of pairs of contractions <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>T</mi>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>T</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(T,T_0)$</annotation>\u0000 </semantics></math>, where the initial operator <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>T</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$T_0$</annotation>\u0000 </semantics></math> is normal, via linear path by reducing the problem to a finite-dimensional one as in the proof of Krein's trace formula by Voiculescu [Oper. Theory Adv. Appl. 24 (1987) 329–332] and Sinha and Mohapatra [Proc. Indian Acad. Sci. Math. Sci. 104 (1994), no. 4, 819–853] and [Integral Equations Operator Theory 24 (1996), no. 3, 285–297]. Consequently, we obtain the Koplienko trace formula for a class of pairs of contractions using the Schäffer matrix unitary dilation. Moreover, we also obtain the Koplienko trace formula for a pair of self-adjoint operators and maximal dissipative operators using the Cayley transform. At the end, we extend the Koplienko–Neidhardt trace formula for a class of pairs of contractions <span></span","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 7","pages":"2581-2608"},"PeriodicalIF":0.8,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. V. Andrade, D. R. Santiago, D. D. Silva, L. C. S. Sobral
<p>We investigate rank 3 instanton vector bundles on <span></span><math> <semantics> <msup> <mi>P</mi> <mn>3</mn> </msup> <annotation>$mathbb {P}^3$</annotation> </semantics></math> of charge <span></span><math> <semantics> <mi>n</mi> <annotation>$n$</annotation> </semantics></math> and its correspondence with rational curves of degree <span></span><math> <semantics> <mrow> <mi>n</mi> <mo>+</mo> <mn>3</mn> </mrow> <annotation>$n+3$</annotation> </semantics></math>. For <span></span><math> <semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>2</mn> </mrow> <annotation>$n=2$</annotation> </semantics></math>, we present a correspondence between stable rank 3 instanton bundles and stable rank 2 reflexive linear sheaves of Chern classes <span></span><math> <semantics> <mrow> <mrow> <mo>(</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>c</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> <annotation>$(c_1,c_2,c_3)=(-1,3,3)$</annotation> </semantics></math> and we use this correspondence to compute the dimension of the family of stable rank 3 instanton bundles of charge 2. Finally, we use the results above to prove that the moduli space of rank 3 instanton bundles on <span></span><math> <semantics> <msup> <mi>P</mi> <mn>3</mn> </msup> <annotation>$mathbb {P}^3$</annotation> </semantics></math> of charge 2 coincides with the moduli space of rank 3 stable locally free sheaves on <span></span><math> <semantics> <msup> <mi>P</mi> <mn>3</mn> </msup> <annotation>$mathbb {P}^3$</annotation> </semantics></math> of Chern cla
{"title":"On rank 3 instanton bundles on \u0000 \u0000 \u0000 P\u0000 3\u0000 \u0000 $mathbb {P}^3$","authors":"A. V. Andrade, D. R. Santiago, D. D. Silva, L. C. S. Sobral","doi":"10.1002/mana.202200332","DOIUrl":"10.1002/mana.202200332","url":null,"abstract":"<p>We investigate rank 3 instanton vector bundles on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <annotation>$mathbb {P}^3$</annotation>\u0000 </semantics></math> of charge <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> and its correspondence with rational curves of degree <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$n+3$</annotation>\u0000 </semantics></math>. For <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$n=2$</annotation>\u0000 </semantics></math>, we present a correspondence between stable rank 3 instanton bundles and stable rank 2 reflexive linear sheaves of Chern classes <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>c</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>c</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>c</mi>\u0000 <mn>3</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>=</mo>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>3</mn>\u0000 <mo>,</mo>\u0000 <mn>3</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$(c_1,c_2,c_3)=(-1,3,3)$</annotation>\u0000 </semantics></math> and we use this correspondence to compute the dimension of the family of stable rank 3 instanton bundles of charge 2. Finally, we use the results above to prove that the moduli space of rank 3 instanton bundles on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <annotation>$mathbb {P}^3$</annotation>\u0000 </semantics></math> of charge 2 coincides with the moduli space of rank 3 stable locally free sheaves on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <annotation>$mathbb {P}^3$</annotation>\u0000 </semantics></math> of Chern cla","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 8","pages":"2814-2827"},"PeriodicalIF":0.8,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Normalized solutions to nonlinear Schrödinger equations with competing Hartree-type nonlinearities","authors":"Divyang Bhimani, Tianxiang Gou, Hichem Hajaiej","doi":"10.1002/mana.202200443","DOIUrl":"10.1002/mana.202200443","url":null,"abstract":"<p>In this paper, we consider solutions to the following nonlinear Schrödinger equation with competing Hartree-type nonlinearities,\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 7","pages":"2543-2580"},"PeriodicalIF":0.8,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Effects of indirect signal absorption in the chemotaxis system involving singularly signal-dependent motilities","authors":"Yan Li, Jiaqi Wang, Fei Pan","doi":"10.1002/mana.202300182","DOIUrl":"10.1002/mana.202300182","url":null,"abstract":"<p>We consider the initial-boundary problem of the chemotaxis system with indirect consumption\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 6","pages":"2036-2046"},"PeriodicalIF":1.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study stability of the three geometric properties: uniform convexity, nearly uniform convexity, and property under the Yoshikawa–Sparr interpolation method when the resulting interpolation space is considered with various equivalent norms. We give an example which shows that interpolation spaces obtained by the discrete and continuous versions of the method need not be isometric and present a method of transferring geometric properties from the discrete case to the continuous one.
{"title":"Convexity properties of Yoshikawa–Sparr interpolation spaces","authors":"Karol Aleksandrowicz, Stanisław Prus","doi":"10.1002/mana.202300388","DOIUrl":"10.1002/mana.202300388","url":null,"abstract":"<p>We study stability of the three geometric properties: uniform convexity, nearly uniform convexity, and property <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>β</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(beta)$</annotation>\u0000 </semantics></math> under the Yoshikawa–Sparr interpolation method when the resulting interpolation space is considered with various equivalent norms. We give an example which shows that interpolation spaces obtained by the discrete and continuous versions of the method need not be isometric and present a method of transferring geometric properties from the discrete case to the continuous one.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 7","pages":"2624-2638"},"PeriodicalIF":0.8,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let denote an isometric immersion of a Kähler manifold with complex dimension into Euclidean space with codimension . We show that generic rank conditions on the second fundamental form of a non-minimal complete real Kähler submanifold imply that is a cylinder over a real Kähler submanifold .
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