Abstract
In Euclidean ([1]) and Hyperbolic ([5]) space, and the round hemisphere ([2]), geodesic balls maximize the gap λ2−λ1 of Dirichlet eigenvalues, among domains with fixed λ1. We prove an upper bound on λ2−λ1 for domains in manifolds with certain curvature bounds. The inequality is sharp on geodesic balls in spaceforms.
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