Some functional inequalities under lower Bakry-Émery-Ricci curvature bounds with ε-range

2022/11/22 by Fujitani, Yasuaki
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.12310

Abstract

For n-dimensional weighted Riemannian manifolds, lower m-Bakry-Émery-Ricci curvature bounds with ε-range, introduced by Lu-Minguzzi-Ohta, integrate constant lower bounds and certain variable lower bounds in terms of weight functions. In this paper, we prove a Cheng type inequality and a local Sobolev inequality under lower m-Bakry-Émery-Ricci curvature bounds with ε-range. These generalize those inequalities under constant curvature bounds for m ∈ (n,∞) to m∈(-∞,1]∪\∞\.

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