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- W56071208 abstract "For a domain Ω contained in a hemisphere of the n-dimensional sphere S n we outline the proof of the optimal result λ2/λ1(Ω) ≤ λ2/λ1 (Ω*) for the ratio of its first two Dirichlet eigenvalues where Ω*, the symmetric rearrangement of Ω in S n , is a geodesic ball in S n having the same n-volume as Ω. Along the way we show that λ2/λ1 for geodesic balls of geodesic radius θ 1 less than or equal to π/2 is an increasing function of θ 1. Our key result is that among all domains contained in a hemisphere of S n and having a fixed value of λ1 the one with the maximal value of λ2 is the geodesic ball of the appropriate radius." @default.
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- W56071208 date "1997-01-01" @default.
- W56071208 modified "2023-09-25" @default.
- W56071208 title "On the Payne-Pólya-Weinberger conjecture on the n-dimensional sphere" @default.
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- W56071208 doi "https://doi.org/10.1007/978-3-0348-8942-1_10" @default.
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