Estimates of eigenvalues of Laplacian by a reduced number of subsets

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$(0,\infty )$. We will also discuss a related conjecture for some universal inequality among eigenvalues of Laplacian.

17pages, to appear in Israel J. Math. arXiv admin note: substantial text overlap with arXiv:1307.3919

References in corpus (1)

• Alexandrov meets Lott--Villani--Sturm