下0权Ricci曲率界下加权流形的几何分析

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-10-09 DOI:10.1016/j.na.2025.113965

Yasuaki Fujitani , Yohei Sakurai

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引用次数: 0

摘要

给出了下0权Ricci曲率界下加权黎曼流形的几何分析。在这样的曲率边界下，证明了紧加权流形上Wang-Xia型的第一个非零Steklov特征值估计，以及封闭加权极小超曲面上Choi-Wang型的第一个非零特征值估计。我们也得到了一个ABP估计和一个Brendle型的Sobolev不等式。

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Geometric analysis on weighted manifolds under lower 0-weighted Ricci curvature bounds

We develop geometric analysis on weighted Riemannian manifolds under lower 0-weighted Ricci curvature bounds. Under such curvature bounds, we prove a first non-zero Steklov eigenvalue estimate of Wang–Xia type on compact weighted manifolds with boundary, and a first non-zero eigenvalue estimate of Choi–Wang type on closed weighted minimal hypersurfaces. We also produce an ABP estimate and a Sobolev inequality of Brendle type.

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来源期刊

Nonlinear Analysis-Theory Methods & Applications 数学-数学

CiteScore

3.30

自引率

0.00%

发文量

265

审稿时长

60 days

期刊介绍： Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.