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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.

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Authors and Affiliations

  1. Division of Mathematics & Research Center for Pure and Applied Mathematics Graduate School of Information Sciences, Tohoku University, 6-3-09 Aramaki-Aza-Aoba, Aoba-ku, Sendai, 980-8579, Japan

    Kei Funano

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  1. Kei Funano
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Correspondence to Kei Funano.

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Supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science.

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Funano, K. Estimates of eigenvalues of the Laplacian by a reduced number of subsets. Isr. J. Math. 217, 413–433 (2017). https://doi.org/10.1007/s11856-017-1453-7

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  • DOI: https://doi.org/10.1007/s11856-017-1453-7

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