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.
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页码：295 / 311
页数：17
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