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Fundamental Gap of Convex Domains in the Spheres (with Appendix B by Qi S. Zhang) (1705.11152v1)
Published 31 May 2017 in math.DG, math.AP, and math.SP
Abstract: In [SWW], 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 $\pi$.
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