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arXiv · 1601.07581

Estimates of eigenvalues of Laplacian by a reduced number of subsets

Kei Funano
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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.

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Kei Funano. 2016-01-27. Estimates of eigenvalues of Laplacian by a reduced number of subsets. https://arxiv.org/abs/1601.07581

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