Estimates of eigenvalues of Laplacian by a reduced number of subsets

2016/01/27 by Funano, Kei
#58C40 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1601.07581

Abstract

Chung-Grigor'yan-Yau's inequality describes upper bounds of eigenvalues of Laplacian in terms of subsets ("input") and their volumes. In this paper we will show that we can reduce "input" in Chung-Grigor'yan-Yau's inequality in the setting of Alexandrov spaces satisfying CD(0,∞). We will also discuss a related conjecture for some universal inequality among eigenvalues of Laplacian.

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