Estimates of eigenvalues of the Laplacian by a reduced number of subsets

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Abstract

Chung–Grigor’yan–Yau’s inequality describes upper bounds of eigenvalues of the 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 the Laplacian.

Original languageEnglish
Pages (from-to)413-433
Number of pages21
JournalIsrael Journal of Mathematics
Volume217
Issue number1
DOIs
Publication statusPublished - 2017 Mar 1

ASJC Scopus subject areas

  • Mathematics(all)

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