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arXiv · 1503.06904

The PPW conjecture in curved spaces

Nick Edelen
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Abstract

In Euclidean and Hyperbolic space, and the hemisphere in $S^n$, geodesic balls maximize the gap $λ_2 - λ_1$ of Dirichlet eigenvalues, amoung domains with fixed $λ_1$. We prove an upper bound on $λ_2 - λ_1$ for domains in manifolds with certain curvature bounds. The inequality is sharp on geodesic balls in spaceforms.

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Nick Edelen. 2016-12-23. The PPW conjecture in curved spaces. https://arxiv.org/abs/1503.06904

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