Pub Date : 2021-12-27DOI: 10.2422/2036-2145.201803_010
Olivia Dumitrescu, Elisa Postinghel
{"title":"Positivity of divisors on blow-up projective spaces, I","authors":"Olivia Dumitrescu, Elisa Postinghel","doi":"10.2422/2036-2145.201803_010","DOIUrl":"https://doi.org/10.2422/2036-2145.201803_010","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"24 1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89406361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-27DOI: 10.2422/2036-2145.202010_035
M. Mastyło, E. B. Silva
{"title":"Interpolation estimates of the measure of noncompactness for multilinear mappings","authors":"M. Mastyło, E. B. Silva","doi":"10.2422/2036-2145.202010_035","DOIUrl":"https://doi.org/10.2422/2036-2145.202010_035","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"94 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78141837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-22DOI: 10.2422/2036-2145.202201_002
Jasmin Horter, T. Lamm, M. Micallef
. In 1981, Sacks and Uhlenbeck introduced their famous α -energy as a way to approxi-mate the Dirichlet energy and produce harmonic maps from surfaces into Riemannian manifolds. However, the second and third authors together with Malchiodi ([11], [12]) showed that for maps between two-spheres this method does not capture every harmonic map. They established a gap theorem for α -harmonic maps of degree zero and also showed that below a certain energy bound α -harmonic maps of degree one are rotations. We establish similar results for ε -harmonic maps u ε : S 2 → S 2 , which are critical points of the ε -energy introduced by the second author in [9]. In particular, we similarly show that ε -harmonic maps of degree zero with energy below 8 π are constant and that maps of degree ± 1 with energy below 12 π are of the form Rx with R ∈ O (3). Moreover, we construct non-trivial ε -harmonic maps of degree zero with energy > 8 π .
{"title":"Rigidity of $varepsilon$-harmonic maps of low degree","authors":"Jasmin Horter, T. Lamm, M. Micallef","doi":"10.2422/2036-2145.202201_002","DOIUrl":"https://doi.org/10.2422/2036-2145.202201_002","url":null,"abstract":". In 1981, Sacks and Uhlenbeck introduced their famous α -energy as a way to approxi-mate the Dirichlet energy and produce harmonic maps from surfaces into Riemannian manifolds. However, the second and third authors together with Malchiodi ([11], [12]) showed that for maps between two-spheres this method does not capture every harmonic map. They established a gap theorem for α -harmonic maps of degree zero and also showed that below a certain energy bound α -harmonic maps of degree one are rotations. We establish similar results for ε -harmonic maps u ε : S 2 → S 2 , which are critical points of the ε -energy introduced by the second author in [9]. In particular, we similarly show that ε -harmonic maps of degree zero with energy below 8 π are constant and that maps of degree ± 1 with energy below 12 π are of the form Rx with R ∈ O (3). Moreover, we construct non-trivial ε -harmonic maps of degree zero with energy > 8 π .","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"104 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75909106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-11DOI: 10.2422/2036-2145.202205_011
A. Bove, M. Mughetti
For $ q $, $ a $ integers such that $ a geq 1 $, $ 1
对于$ q $, $ a $这样的整数，$ a geq 1 $, $ 1
{"title":"Optimal Gevrey regularity for certain sums of squares in two variables","authors":"A. Bove, M. Mughetti","doi":"10.2422/2036-2145.202205_011","DOIUrl":"https://doi.org/10.2422/2036-2145.202205_011","url":null,"abstract":"For $ q $, $ a $ integers such that $ a geq 1 $, $ 1<q $, $ (x, y) in U $, $ U $ a neighborhood of the origin in $ mathbb{R}^{2} $, we consider the operator $$ D_{x}^{2} + x^{2(q-1)} D_{y}^{2} + y^{2a} D_{y}^{2} . $$ Slightly modifying the method of proof of cite{monom} we can see that it is Gevrey $ s_{0} $ hypoelliptic, where $ s_{0}^{-1} = 1 - a^{-1} (q - 1) q^{-1} $. Here we show that this value is optimal, i.e. that there are solutions to $ P u = f $ with $ f $ more regular than $ G^{s_{0}} $ that are not better than Gevrey $ s_{0} $. The above operator reduces to the M'etivier operator (cite{metivier81}) when $ a = 1 $, $ q = 2 $. We give a description of the characteristic manifold of the operator and of its relation with the Treves conjecture on the real analytic regularity for sums of squares.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84059552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-02DOI: 10.2422/2036-2145.202112_003
Francesco Paolo Maiale, Giorgio Tortone, B. Velichkov
Abstract. We give a short and self-contained proof of the Boundary Harnack inequality for a class of domains satisfying some geometric conditions given in terms of a state function that behaves as the distance function to the boundary, is subharmonic inside the domain and satisfies some suitable estimates on the measure of its level sets. We also discuss the applications of this result to some shape optimization and free boundary problems.
{"title":"The Boundary Harnack principle on optimal domains","authors":"Francesco Paolo Maiale, Giorgio Tortone, B. Velichkov","doi":"10.2422/2036-2145.202112_003","DOIUrl":"https://doi.org/10.2422/2036-2145.202112_003","url":null,"abstract":"Abstract. We give a short and self-contained proof of the Boundary Harnack inequality for a class of domains satisfying some geometric conditions given in terms of a state function that behaves as the distance function to the boundary, is subharmonic inside the domain and satisfies some suitable estimates on the measure of its level sets. We also discuss the applications of this result to some shape optimization and free boundary problems.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"65 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90909228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-29DOI: 10.2422/2036-2145.202112_001
Thomas Franzinetti
Given any two K"ahler manifolds $X_1$ and $X_2$, L. Lempert recently proved that if their spaces of K"ahler potentials are isometric with respect to the Mabuchi metric, then $X_1$ and $X_2$ must be diffeomorphic. We prove that this is no longer the case for Sasaki manifolds. Then, considering regular Sasaki manifolds $M_1$ and $M_2$, we prove that if the spaces of potentials are isometric, then $M_1$ and $M_2$ must have, among others, the same universal covering space. Finally, getting rid of the regularity assumption on $M_1$ and $M_2$, we investigate the consequences of the existence of affine Mabuchi isometries: this leads to a family of Sasaki isospectral structures.
给定任意两个K ahler流形$X_1$和$X_2$， L. Lempert最近证明了如果它们的K ahler势的空间相对于Mabuchi度规是等距的，那么$X_1$和$X_2$一定是微分同态的。我们证明这不再是Sasaki流形的情况。然后，考虑正则Sasaki流形$M_1$和$M_2$，证明了如果势空间是等距的，则$M_1$和$M_2$必须具有相同的全称覆盖空间。最后，我们消除了$M_1$和$M_2$上的正则性假设，研究了仿射Mabuchi等距结构存在的结果:由此得到了Sasaki等谱结构族。
{"title":"Isometries of the Space of Sasaki Potentials","authors":"Thomas Franzinetti","doi":"10.2422/2036-2145.202112_001","DOIUrl":"https://doi.org/10.2422/2036-2145.202112_001","url":null,"abstract":"Given any two K\"ahler manifolds $X_1$ and $X_2$, L. Lempert recently proved that if their spaces of K\"ahler potentials are isometric with respect to the Mabuchi metric, then $X_1$ and $X_2$ must be diffeomorphic. We prove that this is no longer the case for Sasaki manifolds. Then, considering regular Sasaki manifolds $M_1$ and $M_2$, we prove that if the spaces of potentials are isometric, then $M_1$ and $M_2$ must have, among others, the same universal covering space. Finally, getting rid of the regularity assumption on $M_1$ and $M_2$, we investigate the consequences of the existence of affine Mabuchi isometries: this leads to a family of Sasaki isospectral structures.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73195149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-10DOI: 10.2422/2036-2145.202010_057
María Carrizosa
{"title":"Décompte de polarisations de degré donné","authors":"María Carrizosa","doi":"10.2422/2036-2145.202010_057","DOIUrl":"https://doi.org/10.2422/2036-2145.202010_057","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84142641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-10DOI: 10.2422/2036-2145.202005_013
Fei Liu
{"title":"On Hilbert’s irreducibility theorem for linear algebraic groups","authors":"Fei Liu","doi":"10.2422/2036-2145.202005_013","DOIUrl":"https://doi.org/10.2422/2036-2145.202005_013","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"62 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81591654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-04DOI: 10.2422/2036-2145.202203_019
P. Cardoso, P. Gonccalves, Byron Jim'enez-Oviedo
In this article we analyse the hydrodynamical behavior of the symmetric exclusion process with long jumps and in the presence of a slow barrier. The jump rates for fast bonds are given by a transition probability $p(cdot)$ which is symmetric and has finite variance, while for slow bonds the jump rates are given $p(cdot)alpha n^{-beta}$ (with $alpha>0$ and $betageq 0$), and correspond to jumps from $mathbb{Z}_{-}^{*}$ to $mathbb N$. We prove that: if there is a fast bond from $mathbb{Z}_{-}^{*}$ and $mathbb N$, then the hydrodynamic limit is given by the heat equation with no boundary conditions; otherwise, it is given by the previous equation if $0leq beta<1$, but for $betageq 1$ boundary conditions appear, namely, we get Robin (linear) boundary conditions if $beta=1$ and Neumann boundary conditions if $beta>1$.
{"title":"Hydrodynamic behavior of long-range symmetric exclusion with a slow barrier: superdiffusive regime","authors":"P. Cardoso, P. Gonccalves, Byron Jim'enez-Oviedo","doi":"10.2422/2036-2145.202203_019","DOIUrl":"https://doi.org/10.2422/2036-2145.202203_019","url":null,"abstract":"In this article we analyse the hydrodynamical behavior of the symmetric exclusion process with long jumps and in the presence of a slow barrier. The jump rates for fast bonds are given by a transition probability $p(cdot)$ which is symmetric and has finite variance, while for slow bonds the jump rates are given $p(cdot)alpha n^{-beta}$ (with $alpha>0$ and $betageq 0$), and correspond to jumps from $mathbb{Z}_{-}^{*}$ to $mathbb N$. We prove that: if there is a fast bond from $mathbb{Z}_{-}^{*}$ and $mathbb N$, then the hydrodynamic limit is given by the heat equation with no boundary conditions; otherwise, it is given by the previous equation if $0leq beta<1$, but for $betageq 1$ boundary conditions appear, namely, we get Robin (linear) boundary conditions if $beta=1$ and Neumann boundary conditions if $beta>1$.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81844673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-19DOI: 10.2422/2036-2145.202111_021
S. Daneri, Eris Runa
We show striped pattern formation in the large volume limit for a class of generalized antiferromagnetic local/nonlocal interaction functionals in general dimension previously considered Goldman-Runa and Daneri-Runa and in Giuliani-Lieb-Lebowitz and Giuliani-Seiringer in the discrete setting. In such a model the relative strength between the short range attractive term favouring pure phases and the long range repulsive term favouring oscillations is modulated by a parameter $tau$. For $tau<0$ minimizers are trivial uniform states. It is conjectured that $forall,dgeq2$ there exists $00$ minimizers are striped/lamellar patterns. In Daneri-Runa arXiv:1702.07334 the authors prove the above for $L=2kh^*_tau$, where $kinN$ and $h^*_tau$ is the optimal period of stripes for a given $0
{"title":"Periodic striped configurations in the large volume limit","authors":"S. Daneri, Eris Runa","doi":"10.2422/2036-2145.202111_021","DOIUrl":"https://doi.org/10.2422/2036-2145.202111_021","url":null,"abstract":"We show striped pattern formation in the large volume limit for a class of generalized antiferromagnetic local/nonlocal interaction functionals in general dimension previously considered Goldman-Runa and Daneri-Runa and in Giuliani-Lieb-Lebowitz and Giuliani-Seiringer in the discrete setting. In such a model the relative strength between the short range attractive term favouring pure phases and the long range repulsive term favouring oscillations is modulated by a parameter $tau$. For $tau<0$ minimizers are trivial uniform states. It is conjectured that $forall,dgeq2$ there exists $0<bar{tau}ll1$ such that for all $0<tauleqbar{tau}$ and for all $L>0$ minimizers are striped/lamellar patterns. In Daneri-Runa arXiv:1702.07334 the authors prove the above for $L=2kh^*_tau$, where $kinN$ and $h^*_tau$ is the optimal period of stripes for a given $0<tauleqbar{tau}$. The purpose of this paper is to show the validity of the conjecture for generic $L$.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85175672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：