Mathematische Annalen最新文献

Coarsely holomorphic curves and symplectic topology 粗全形曲线与交映拓扑学

IF 1.4 2区数学

Mathematische Annalen Pub Date : 2024-09-19 DOI: 10.1007/s00208-024-02985-8

Spencer Cattalani

引用次数: 0

Multifractality and intermittency in the limit evolution of polygonal vortex filaments 多边形涡旋丝极限演化中的多分形和间歇性

IF 1.4 2区数学

Mathematische Annalen Pub Date : 2024-09-17 DOI: 10.1007/s00208-024-02971-0

Valeria Banica, Daniel Eceizabarrena, Andrea R. Nahmod, Luis Vega

引用次数: 0

On the uniqueness of periodic solutions for a Rayleigh–Liénard system with impulses 论带脉冲的 Rayleigh-Liénard 系统周期解的唯一性

IF 1.4 2区数学

Mathematische Annalen Pub Date : 2024-09-17 DOI: 10.1007/s00208-024-02996-5

Hebai Chen, Jie Jin, Zhaoxia Wang, Dongmei Xiao

引用次数: 0

Uniformly super McDuff $$hbox {II}_1$$ factors 统一超麦克杜夫 $$hbox {II}_1$$ 因子

IF 1.4 2区数学

Mathematische Annalen Pub Date : 2024-09-12 DOI: 10.1007/s00208-024-02959-w

Isaac Goldbring, David Jekel, Srivatsav Kunnawalkam Elayavalli, Jennifer Pi

引用次数: 0

Normalized solutions for Kirchhoff equations with Sobolev critical exponent and mixed nonlinearities 具有索波列夫临界指数和混合非线性的基尔霍夫方程的归一化解

IF 1.4 2区数学

Mathematische Annalen Pub Date : 2024-09-12 DOI: 10.1007/s00208-024-02982-x

Sitong Chen, Xianhua Tang

{"title":"Normalized solutions for Kirchhoff equations with Sobolev critical exponent and mixed nonlinearities","authors":"Sitong Chen, Xianhua Tang","doi":"10.1007/s00208-024-02982-x","DOIUrl":"https://doi.org/10.1007/s00208-024-02982-x","url":null,"abstract":"This paper focuses on the existence of normalized solutions for the following Kirchhoff equation: $$begin{aligned} left{ begin{array}{ll} -left( a+bint _{{mathbb {R}}^3}|nabla u|^2textrm{d}xright) Delta u+lambda u=u^5+mu |u|^{q-2}u, & xin {mathbb {R}}^3, int _{{mathbb {R}}^3}u^2textrm{d}x=c, end{array} right. end{aligned}$$where (a,b,c>0), (mu in {mathbb {R}}) and (2<q<6), (lambda in {mathbb {R}}) will arise as a Lagrange multiplier that is not a priori given. By using new analytical techniques, the paper establishes several existence results for the case (mu >0): <ol>\u0000<li>\u0000(1)\u0000The existence of two solutions, one being a local minimizer and the other of mountain-pass type, under explicit conditions on c when (2<q<frac{10}{3}).\u0000</li>\u0000<li>\u0000(2)\u0000The existence of a mountain-pass type solution under explicit conditions on c when (frac{10}{3}le q<frac{14}{3}).\u0000</li>\u0000<li>\u0000(3)\u0000The existence of a ground state solution for all (c>0) when (frac{14}{3}le q<6).\u0000</li>\u0000</ol> Furthermore, the paper presents the first non-existence result for the case (mu le 0) and (2<q<6). In particular, refined estimates of energy levels are proposed, suggesting a new threshold of compactness in the (L^2)-constraint. This study addresses an open problem for (2<q<frac{10}{3}) and fills a gap in the case (frac{10}{3}le q<frac{14}{3}). We believe that our approach can be applied to a broader range of nonlinear terms with Sobolev critical growth, and the underlying ideas have potential for future development and applicability.","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"158 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Gaussian estimates vs. elliptic regularity on open sets 开放集上的高斯估计与椭圆正则性

IF 1.4 2区数学

Mathematische Annalen Pub Date : 2024-09-10 DOI: 10.1007/s00208-024-02939-0

Tim Böhnlein, Simone Ciani, Moritz Egert

引用次数: 0

Radial symmetry and sharp asymptotic behaviors of nonnegative solutions to $$D^{1,p}$$ -critical quasi-linear static Schrödinger–Hartree equation involving p-Laplacian $$-Delta _{p}$$ 涉及 p-Laplacian $$-Delta _{p}$$ 的 $$D^{1,p}$ 临界准线性静态薛定谔-哈特里方程的非负解的径向对称性和尖锐渐近行为

IF 1.4 2区数学

Mathematische Annalen Pub Date : 2024-09-09 DOI: 10.1007/s00208-024-02986-7

Wei Dai, Yafei Li, Zhao Liu

{"title":"Radial symmetry and sharp asymptotic behaviors of nonnegative solutions to $$D^{1,p}$$ -critical quasi-linear static Schrödinger–Hartree equation involving p-Laplacian $$-Delta _{p}$$","authors":"Wei Dai, Yafei Li, Zhao Liu","doi":"10.1007/s00208-024-02986-7","DOIUrl":"https://doi.org/10.1007/s00208-024-02986-7","url":null,"abstract":"In this paper, we mainly consider nonnegative weak solution to the (D^{1,p}(mathbb {R}^{N}))-critical quasi-linear static Schrödinger–Hartree equation with p-Laplacian (-Delta _{p}) and nonlocal nonlinearity: $$begin{aligned} -Delta _p u =left( |x|^{-2p}*|u|^{p}right) |u|^{p-2}u qquad&text{ in } ,, mathbb {R}^N, end{aligned}$$where (1<p<frac{N}{2}), (Nge 3) and (uin D^{1,p}(mathbb {R}^N)). First, we establish regularity and the sharp estimates on asymptotic behaviors for any positive solution u (and (|nabla u|)) to more general equation (-Delta _p u=V(x)u^{p-1}) with (Vin L^{frac{N}{p}}(mathbb {R}^{N})). Then, as a consequence, we can apply the method of moving planes to prove that all the nontrivial nonnegative solutions are radially symmetric and strictly decreasing about some point (x_0in mathbb {R}^N). The radial symmetry and sharp asymptotic estimates for more general nonlocal quasi-linear equations were also included.","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"5 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Rigid comparison geometry for Riemannian bands and open incomplete manifolds 黎曼带和开放不完全流形的刚性比较几何

IF 1.4 2区数学

Mathematische Annalen Pub Date : 2024-09-05 DOI: 10.1007/s00208-024-02973-y

Sven Hirsch, Demetre Kazaras, Marcus Khuri, Yiyue Zhang

{"title":"Rigid comparison geometry for Riemannian bands and open incomplete manifolds","authors":"Sven Hirsch, Demetre Kazaras, Marcus Khuri, Yiyue Zhang","doi":"10.1007/s00208-024-02973-y","DOIUrl":"https://doi.org/10.1007/s00208-024-02973-y","url":null,"abstract":"Comparison theorems are foundational to our understanding of the geometric features implied by various curvature constraints. This paper considers manifolds with a positive lower bound on either scalar, 2-Ricci, or Ricci curvature, and contains a variety of theorems which provide sharp relationships between this bound and notions of width. Some inequalities leverage geometric quantities such as boundary mean curvature, while others involve topological conditions in the form of linking requirements or homological constraints. In several of these results open and incomplete manifolds are studied, one of which partially addresses a conjecture of Gromov in this setting. The majority of results are accompanied by rigidity statements which isolate various model geometries—both complete and incomplete—including a new characterization of round lens spaces, and other models that have not appeared elsewhere. As a byproduct, we additionally give new and quantitative proofs of several classical comparison statements such as Bonnet-Myers’ and Frankel’s Theorem, as well as a version of Llarull’s Theorem and a notable fact concerning asymptotically flat manifolds. The results that we present vary significantly in character, however a common theme is present in that the lead role in each proof is played by spacetime harmonic functions, which are solutions to a certain elliptic equation originally designed to study mass in mathematical general relativity.","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"309 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On neighborhoods of embedded complex tori 关于内嵌复杂环的邻域

IF 1.4 2区数学

Mathematische Annalen Pub Date : 2024-09-03 DOI: 10.1007/s00208-024-02975-w

Xianghong Gong, Laurent Stolovitch

引用次数: 0

Extensions of k-regulous functions from two-dimensional varieties 来自二维变体的 k-regulous 函数的扩展

IF 1.4 2区数学

Mathematische Annalen Pub Date : 2024-09-03 DOI: 10.1007/s00208-024-02981-y

Juliusz Banecki

引用次数: 0