Communications in Contemporary Mathematics最新文献

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Complete CMC-1 surfaces in hyperbolic space with arbitrary complex structure 双曲空间中具有任意复杂结构的完整 CMC-1 曲面

IF 1.6 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics

Pub Date : 2024-04-10 DOI: 10.1142/s0219199724500111

Antonio Alarcón, Ildefonso Castro-Infantes, Jorge Hidalgo

We prove that every open Riemann surface $M$ is the complex structure of a complete surface of constant mean curvature $1$ ( $CMC-1$ ) in the three-dimensional hyperbolic space $ℍ^{3}$ . We go further and establish a jet interpolation theorem for complete conformal $CMC-1$ immersions $M \to ℍ^{3}$ . As a consequence, we show the existence of complete densely immersed $CMC-1$ surfaces in $ℍ^{3}$ with arbitrary complex structure. We obtain these results as application of a uniform approximation theorem with jet interpolation for holomorphic null curves in $ℂ^{2} \times ℂ^{*}$ which is also established in this paper.

我们证明了每个开放黎曼曲面 M 都是三维双曲空间ℍ3 中恒定平均曲率 1（CMC-1）完全曲面的复结构。我们进一步建立了完全保角 CMC-1 沉浸 M→ℍ3 的射流插值定理。因此，我们证明了在ℍ3 中存在具有任意复杂结构的完全密集浸入的 CMC-1 曲面。我们将这些结果应用于本文同样建立的针对ℂ2×ℂ∗中全形空曲线的喷射插值的均匀逼近定理。

引用次数: 0

Shadowing, Hyers–Ulam stability and hyperbolicity for nonautonomous linear delay differential equations 非自治线性延迟微分方程的阴影、海尔-乌兰稳定性和双曲性

IF 1.6 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics

Pub Date : 2024-03-27 DOI: 10.1142/s0219199724500123

Lucas Backes, Davor Dragičević, Mihály Pituk

It is known that hyperbolic nonautonomous linear delay differential equations in a finite dimensional space are Hyers–Ulam stable and hence shadowable. The converse result is available only in the special case of autonomous and periodic linear delay differential equations with a simple spectrum. In this paper, we prove the converse and hence the equivalence of all three notions in the title for a general class of nonautonomous linear delay differential equations with uniformly bounded coefficients. The importance of the boundedness assumption is shown by an example.

众所周知，有限维空间中的双曲非自治线性延迟微分方程是海尔-乌兰稳定的，因此是可影的。只有在具有简单谱的自洽周期线性延迟微分方程的特殊情况下，才有相反的结果。在本文中，我们证明了反向结果，进而证明了标题中所有三个概念对于一类具有均匀有界系数的非自治线性延迟微分方程的等价性。有界性假设的重要性将通过一个例子来说明。

引用次数: 0

Compactified Jacobians of extended ADE curves and Lagrangian fibrations 扩展 ADE 曲线和拉格朗日纤维的紧凑雅各比

IF 1.6 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics

Pub Date : 2024-03-09 DOI: 10.1142/s0219199724500044

Adam Czapliński, Andreas Krug, Manfred Lehn, Sönke Rollenske

We observe that general reducible curves in sufficiently positive linear systems on K3 surfaces are of a form that generalize Kodaira’s classification of singular elliptic fibers and thus call them extended ADE curves. On such a curve $C$ , we describe a compactified Jacobian and show that its components reflect the intersection graph of $C$ . This extends known results when $C$ is reduced, but new difficulties arise when $C$ is non-reduced. As an application, we get an explicit description of general singular fibers of certain Lagrangian fibrations of Beauville–Mukai type.

我们观察到，K3 曲面上充分正线性系统中的一般可还原曲线的形式概括了小平的奇异椭圆纤维分类，因此称其为扩展 ADE 曲线。在这样的曲线 C 上，我们描述了一个紧凑化的雅各比，并证明其分量反映了 C 的交点图。这扩展了 C 被还原时的已知结果，但在 C 未被还原时又出现了新的困难。作为应用，我们得到了对某些博维尔-穆凯类型拉格朗日纤维的一般奇异纤维的明确描述。

引用次数: 0

A global Morse index theorem and applications to Jacobi fields on CMC surfaces 全局莫尔斯指数定理及其在 CMC 表面雅可比场上的应用

IF 1.6 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics

Pub Date : 2024-02-28 DOI: 10.1142/s0219199723500645

Wu-Hsiung Huang

In this paper, we establish a “global” Morse index theorem. Given a hypersurface <math altimg="eq-00001.gif" display="inline" overflow="scroll"><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math> of constant mean curvature, immersed in <math altimg="eq-00002.gif" display="inline" overflow="scroll"><msup><mrow><mi>ℝ</mi></mrow><mrow><mi>n</mi><mo stretchy="false">+</mo><mn>1</mn></mrow></msup></math>. Consider a continuous deformation of “generalized” Lipschitz domain <math altimg="eq-00003.gif" display="inline" overflow="scroll"><mi>D</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> enlarging in <math altimg="eq-00004.gif" display="inline" overflow="scroll"><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math>. The topological type of <math altimg="eq-00005.gif" display="inline" overflow="scroll"><mi>D</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> is permitted to change along <math altimg="eq-00006.gif" display="inline" overflow="scroll"><mi>t</mi></math>, so that <math altimg="eq-00007.gif" display="inline" overflow="scroll"><mi>D</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> has an arbitrary shape which can “reach afar” in <math altimg="eq-00008.gif" display="inline" overflow="scroll"><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math>, i.e. cover any preassigned area. The proof of the global Morse index theorem is reduced to the continuity in <math altimg="eq-00009.gif" display="inline" overflow="scroll"><mi>t</mi></math> of the Sobolev space <math altimg="eq-00010.gif" display="inline" overflow="scroll"><msub><mrow><mi>H</mi></mrow><mrow><mi>t</mi></mrow></msub></math> of variation functions on <math altimg="eq-00011.gif" display="inline" overflow="scroll"><mi>D</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math>, as well as the continuity of eigenvalues of the stability operator. We devise a “detour” strategy by introducing a notion of “set-continuity” of <math altimg="eq-00012.gif" display="inline" overflow="scroll"><mi>D</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> in <math altimg="eq-00013.gif" display="inline" overflow="scroll"><mi>t</mi></math> to yield the required continuities of <math altimg="eq-00014.gif" display="inline" overflow="scroll"><msub><mrow><mi>H</mi></mrow><mrow><mi>t</mi></mrow></msub></math> and of eigenvalues. The global Morse index theorem thus follows and provides a structural theorem of the existence of Jacobi fields on domains in <math altimg="eq-00015.gif" display="

在本文中，我们建立了一个 "全局 "莫尔斯指数定理。给定一个浸没在ℝn+1 中的恒定平均曲率超曲面 Mn。考虑在 Mn 中放大的 "广义 "Lipschitz 域 D(t) 的连续变形。允许 D(t) 的拓扑类型沿 t 变化，因此 D(t) 具有任意形状，可以在 Mn 中 "到达远处"，即覆盖任何预分配区域。全局莫尔斯指数定理的证明简化为 D(t) 上变化函数的索波列夫空间 Ht 在 t 中的连续性，以及稳定算子特征值的连续性。我们设计了一种 "迂回 "策略，即引入 D(t) 在 t 中的 "集合连续性 "概念，从而得到所需的 Ht 连续性和特征值连续性。全局莫尔斯指数定理由此而来，并提供了关于 Mn 域上雅各比场存在性的结构定理。

引用次数: 0

Toroidal extended affine Lie algebras and vertex algebras 环状扩展仿射李代数和顶点代数

IF 1.6 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics

Pub Date : 2024-02-23 DOI: 10.1142/s0219199724500032

Fulin Chen, Haisheng Li, Shaobin Tan

In this paper, we study nullity- $2$ toroidal extended affine Lie algebras in the context of vertex algebras and their $ϕ$ -coordinated modules. Among the main results, we introduce a variant of toroidal extended affine Lie algebras, associate vertex algebras to the variant Lie algebras, and establish a canonical connection between modules for toroidal extended affine Lie algebras and $ϕ$ -coordinated modules for these vertex algebras. Furthermore, by employing some results of Billig, we obtain an explicit realization of a class of irreducible modules for the variant Lie algebras.

在本文中，我们在顶点代数及其ϕ协调模块的背景下研究了空性-2环形扩展仿射李代数。在主要结果中，我们引入了环状扩展仿射李代数的一个变体，将顶点代数与变体李代数联系起来，并在环状扩展仿射李代数的模块与这些顶点代数的 ϕ 配位模块之间建立了典范联系。此外，通过运用比立格的一些结果，我们得到了变体李代数的一类不可还原模块的明确实现。

引用次数: 0

Concentration phenomena for the fractional relativistic Schrödinger–Choquard equation 分数相对论薛定谔-乔夸德方程的集中现象

IF 1.6 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics

Pub Date : 2024-02-23 DOI: 10.1142/s021919972350061x

Vincenzo Ambrosio

We consider the fractional relativistic Schrödinger–Choquard equation <disp-formula-group><math altimg="eq-00001.gif" display="block" overflow="scroll"><mrow><mfenced close="" open="{" separators=""><mrow><mtable columnlines="none" equalcolumns="false" equalrows="false"><mtr><mtd columnalign="left"><msup><mrow><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mi mathvariant="normal">Δ</mi><mo stretchy="false">+</mo><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy="false">)</mo></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mo stretchy="false">+</mo><mi>V</mi><mo stretchy="false">(</mo><mi>𝜀</mi><mi>x</mi><mo stretchy="false">)</mo><mi>u</mi><mo>=</mo><mfenced close=")" open="(" separators=""><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>μ</mi></mrow></msup></mrow></mfrac><mo stretchy="false">∗</mo><mi>F</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo></mrow></mfenced><mi>f</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo></mtd><mtd columnalign="left"><mstyle><mtext>in</mtext></mstyle><mspace width=".17em"></mspace><mspace width=".17em"></mspace><msup><mrow><mi>ℝ</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd columnalign="left"><mi>u</mi><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mo stretchy="false">(</mo><msup><mrow><mi>ℝ</mi></mrow><mrow><mi>N</mi></mrow></msup><mo stretchy="false">)</mo><mo>,</mo></mtd><mtd columnalign="left"><mi>u</mi><mo>></mo><mn>0</mn><mspace width=".17em"></mspace><mspace width=".17em"></mspace><mstyle><mtext>in</mtext></mstyle><mspace width=".17em"></mspace><mspace width=".17em"></mspace><msup><mrow><mi>ℝ</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></mrow></math></disp-formula-group> where <math altimg="eq-00002.gif" display="inline" overflow="scroll"><mi>𝜀</mi><mo>></mo><mn>0</mn></math> is a small parameter, <math altimg="eq-00003.gif" display="inline" overflow="scroll"><mi>s</mi><mo>∈</mo><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo stretchy="false">)</mo></math>, <math altimg="eq-00004.gif" display="inline" overflow="scroll"><mi>m</mi><mo>></mo><mn>0</mn></math>, <math altimg="eq-00005.gif" display="inline" overflow="scroll"><mi>N</mi><mo>></mo><mn>2</mn><mi>s</mi></math>, <math altimg="eq-00006.gif" display="inline" overflow="scroll"><mi>μ</mi><mo>∈</mo><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mi>s</mi><mo stretchy="false">)</mo></math>, <math altimg="eq-00007.gif" display="inline" overflow="scroll"><msup><mrow><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mi mathvariant="normal">Δ</mi><mo stretchy="false">+</mo><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy=

我们考虑分数相对论薛定谔-乔夸德方程 (-Δ+m2)su+V(𝜀x)u=1|x|μ∗F(u)f(u)inℝN,u∈Hs(ℝN),u>；0inℝN，其中𝜀>0是一个小参数，s∈(0,1)，m>0，N>2s，μ∈(0,2s)，(-Δ+m2)s是分数相对论薛定谔算子，V：V: ℝN→ℝ是具有局部最小值的连续势，f:ℝ→ℝ是在无穷远处具有亚临界增长的连续非线性，F(t)=∫0tf(τ)dτ。利用适当的变分论证，我们构建了一系列解，这些解集中在𝜀→0 时 V 的局部最小值附近。

引用次数: 0

Weight module classifications for Bershadsky–Polyakov algebras 贝尔沙德斯基-波利亚科夫代数的权重模块分类

IF 1.6 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics

Pub Date : 2024-02-23 DOI: 10.1142/s0219199723500633

Dražen Adamović, Kazuya Kawasetsu, David Ridout

The Bershadsky–Polyakov algebras are the subregular quantum Hamiltonian reductions of the affine vertex operator algebras associated with ${𝔰 𝔩}_{3}$ . In (D. Adamović, K. Kawasetsu and D. Ridout, A realisation of the Bershadsky–Polyakov algebras and their relaxed modules, Lett. Math. Phys.111 (2021) 38, arXiv:2007.00396 [math.QA]), we realized these algebras in terms of the regular reduction, Zamolodchikov’s W₃-algebra, and an isotropic lattice vertex operator algebra. We also proved that a natural construction of relaxed highest-weight Bershadsky–Polyakov modules has the property that the result is generically irreducible. Here, we prove that this construction, when combined with spectral flow twists, gives a complete set of irreducible weight modules whose weight spaces are finite-dimensional. This gives a simple independent proof of the main classification theorem of (Z. Fehily, K. Kawasetsu and D. Ridout, Classifying relaxed highest-weight modules for admissible-level Bershadsky–Polyakov algebras, Comm. Math. Phys.385 (2021) 859–904, arXiv:2007.03917 [math.RT]) for nondegenerate admissible levels and extends this classification to a category of weight modules. We also deduce the classification for the nonadmissible level $k = - \frac{7}{3}$ , which is new.

伯沙德斯基-波利亚科夫代数是与𝔰𝔩3 相关的仿射顶点算子代数的亚规则量子哈密顿还原。在 (D. Adamović、K. Kawasetsu 和 D. Ridout, A realisation of the Bershadsky-Polyakov algebras and their relaxed modules, Lett.Math.Phys.111（2021）38，arXiv:2007.00396 [math.QA]），我们用正则还原、扎莫洛奇科夫的 W3-代数和等向晶格顶点算子代数实现了这些代数。我们还证明了松弛的最高权布尔夏德斯基-波利亚科夫模块的自然构造具有结果一般不可还原的性质。在这里，我们证明了当这种构造与谱流捻合相结合时，可以得到一组完整的不可还原权重模块，其权重空间是有限维的。这给出了 (Z. Fehily, K. Kawasetsu and D. Ridout, Classifying relaxed highest-weight modules for admissible-level Bershadsky-Polyakov algebras, Comm. Math.Math.Phys.385（2021）859-904，arXiv:2007.03917 [math.RT]），并将此分类扩展到权重模块类别。我们还推导出了新的非可容许级 k=-73 的分类。

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引用次数: 0

Geodesics on adjoint orbits of SL(n, ℝ) SL(n, ℝ) 邻接轨道上的测地线

IF 1.6 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics

Pub Date : 2024-02-23 DOI: 10.1142/s0219199724500019

Brian Grajales, Lino Grama, Rafaela F. Prado

In this paper, we examine the geodesics on adjoint orbits of $SL (n, ℝ)$ that are equipped with $SO (n)$ -invariant metrics, where $SO (n)$ is the maximal compact subgroup. Our primary technique involves translating this problem into a geometric problem in the tangent bundle of certain $SO (n)$ -flag manifolds and describing the geodesic equations with respect to the Sasaki metric on the tangent bundle. Additionally, we utilize tools from Lie Theory to obtain explicit descriptions of families of geodesics. We provide a detailed analysis of the case for $SL (2, ℝ)$ .

在本文中，我们研究了SL(n,ℝ)邻接轨道上的大地线，这些轨道配备了SO(n)不变度量，其中SO(n)是最大紧凑子群。我们的主要技术包括将这一问题转化为某些 SO(n)-flag 流形切线束中的几何问题，并描述切线束上有关佐佐木度量的大地方程。此外，我们还利用 Lie Theory 的工具获得了对大地方程组的明确描述。我们详细分析了 SL(2,ℝ) 的情况。

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引用次数: 0

Perspective functions with nonlinear scaling 非线性缩放透视函数

IF 1.6 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics

Pub Date : 2024-02-19 DOI: 10.1142/s0219199723500657

Luis M. Briceño-Arias, Patrick L. Combettes, Francisco J. Silva

The classical perspective of a function is a construction which transforms a convex function into one that is jointly convex with respect to an auxiliary scaling variable. Motivated by applications in several areas of applied analysis, we investigate an extension of this construct in which the scaling variable is replaced by a nonlinear term. Our construction is placed in the general context of locally convex spaces and it generates a lower semicontinuous convex function under broad assumptions on the underlying functions. Various convex-analytical properties are established and closed-form expressions are derived. Several applications are presented.

函数的经典视角是一种构造，它将凸函数转化为一个与辅助缩放变量共凸的函数。受应用分析多个领域应用的启发，我们研究了这一构造的扩展，其中缩放变量被一个非线性项所取代。我们的构造被置于局部凸空间的一般背景下，并在对基础函数的宽泛假设下产生了低半连续凸函数。我们建立了各种凸分析特性，并导出了闭式表达式。还介绍了一些应用。

引用次数: 0

Well-posedness and analyticity of solutions for the sixth-order Boussinesq equation 六阶布辛斯方程的良好求解和解析性

IF 1.6 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics

Pub Date : 2024-02-16 DOI: 10.1142/s0219199724500056

Amin Esfahani, Achenef Tesfahun

In this paper, the sixth-order Boussinesq equation is studied. We extend the local well-posedness theory for this equation with quadratic and cubic nonlinearities to the high dimensional case. In spite of having the “bad” fourth term $Δ u$ in the equation, we derive some dispersive estimates leading to the existence of local solutions which also improves the previous results in the cubic case. In addition, we show persistence of spatial analyticity of solutions for the cubic nonlinearity.

本文研究了六阶布辛斯方程。我们将该方程的二次方和三次方非线性的局部好求解理论扩展到高维情况。尽管方程中存在 "坏 "的第四项 Δu，我们仍推导出了一些分散估计值，从而得出了局部解的存在性，这也改进了之前三次方程的结果。此外，我们还展示了立方非线性解的空间解析性的持久性。

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Communications in Contemporary Mathematics

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