第一个 Dirichlet 特征值和宽度

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2024-10-23 DOI:10.1016/j.jfa.2024.110709

Guoyi Xu

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引用次数: 0

摘要

对于具有非负 Ricci 曲率和平均凸边界的测地球，已知该测地球的第一个 Dirichlet 特征值有一个与其半径相关的尖锐下界。我们展示了一个定量的显式不等式，它用第一个 Dirichlet 特征值与相应的尖锐下界之间的谱差距来约束测地球的宽度。

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The first Dirichlet eigenvalue and the width

For a geodesic ball with non-negative Ricci curvature and mean convex boundary, it is known that the first Dirichlet eigenvalue of this geodesic ball has a sharp lower bound in term of its radius. We show a quantitative explicit inequality, which bounds the width of geodesic ball in terms of the spectral gap between the first Dirichlet eigenvalue and the corresponding sharp lower bound.

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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis