Mathematische Annalen最新文献_第2页

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

Mappings of finite distortion on metric surfaces 度量曲面上的有限变形映射