A REVERSE HOLDER INEQUALITY FOR FIRST EIGENFUNCTIONS OF THE DIRICHLET LAPLACIAN ON RCD(K, N) SPACES

被引：1

作者：

Gunes, Mustafa Alper ^{[1
]}

Mondino, Andrea ^{[1
]}

机构：

[1] Univ Oxford, Math Inst, Radcliffe Observ, Andrew Wiles Bldg,Woodstock Rd, Oxford OX2 6GG, England

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 151卷 / 01期

基金：

欧洲研究理事会;

关键词：

METRIC-MEASURE-SPACES; RICCI CURVATURE; ISOPERIMETRIC-INEQUALITIES; RIEMANNIAN-MANIFOLDS; EQUIVALENCE; EIGENVALUES; GEOMETRY; BOUNDS; SHARP;

D O I：

10.1090/proc/16099

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the framework of (possibly non-smooth) metric measure spaces with Ricci curvature bounded below by a positive constant in a synthetic sense, we establish a sharp and rigid reverse-Holder inequality for first eigenfunctions of the Dirichlet Laplacian. This generalises to the positively curved and non-smooth setting the classical "Chiti Comparison Theorem". We also prove a related quantitative stability result which seems to be new even for smooth Riemannian manifolds.

引用

页码：295 / 311

页数：17

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