Fundamental Gap of Convex Domains in the Spheres

S. Seto, L. Wang, and G. Wei proved that the gap between the first two Dirichlet eigenvalues of a convex domain in the unit sphere is at least as large as that for an associated operator on an interval with the same diameter, provided that the domain has the diameter at most $\pi/2$. In this paper,...

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Bibliographic Details
Published inAmerican journal of mathematics Vol. 142; no. 4; pp. 1161 - 1191
Main Authors He, Chenxu, Wei, Guofang, Zhang, Qi S
Format Journal Article
LanguageEnglish
Published Baltimore Johns Hopkins University Press 01.08.2020
Subjects
Dirichlet problem
Domains
Eigenvalues
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Summary:S. Seto, L. Wang, and G. Wei proved that the gap between the first two Dirichlet eigenvalues of a convex domain in the unit sphere is at least as large as that for an associated operator on an interval with the same diameter, provided that the domain has the diameter at most $\pi/2$. In this paper, we extend Seto-Wang-Wei's result to convex domains in the unit sphere with diameter less than $\pi$.
ISSN:0002-9327
1080-6377
1080-6377
DOI:10.1353/ajm.2020.0033