Estimates of eigenvalues of Laplacian by a reduced number of subsets
classification
🧮 math.DG
keywords
eigenvaluesinequalitylaplacianchung-grigorinputsubsetswillyan-yau
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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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