Two balls maximize the third Neumann eigenvalue in hyperbolic space

Pedro Freitas; Richard Snyder Laugesen

doi:10.2422/2036-2145.202010_059

Two balls maximize the third Neumann eigenvalue in hyperbolic space

Pedro Freitas
, Richard Snyder Laugesen

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the third eigenvalue of the Neumann Laplacian in hyperbolic space is maximal for the disjoint union of two geodesic balls, among domains of given volume. This extends a recent result by Bucur and Henrot in Euclidean space, while providing a new proof of a key step in their argument.

Original language	English (US)
Pages (from-to)	1325-1355
Number of pages	31
Journal	Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Volume	23
Issue number	3
DOIs	https://doi.org/10.2422/2036-2145.202010_059
State	Published - 2022

ASJC Scopus subject areas

Theoretical Computer Science
Mathematics (miscellaneous)

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10.2422/2036-2145.202010_059

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title = "Two balls maximize the third Neumann eigenvalue in hyperbolic space",

abstract = "We show that the third eigenvalue of the Neumann Laplacian in hyperbolic space is maximal for the disjoint union of two geodesic balls, among domains of given volume. This extends a recent result by Bucur and Henrot in Euclidean space, while providing a new proof of a key step in their argument.",

author = "Pedro Freitas and Laugesen, \{Richard Snyder\}",

note = "This research was supported by the Fundac¸{\~a}o para a Ci{\^e}ncia e a Tecnologia (Portugal) through project UIDB/00208/2020 (Pedro Freitas), and a grant from the Simons Foundation (\#429422 to Richard Laugesen). Received October 19, 2020; accepted April 22, 2021. Published online September 2022.",

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AB - We show that the third eigenvalue of the Neumann Laplacian in hyperbolic space is maximal for the disjoint union of two geodesic balls, among domains of given volume. This extends a recent result by Bucur and Henrot in Euclidean space, while providing a new proof of a key step in their argument.

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Two balls maximize the third Neumann eigenvalue in hyperbolic space

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