The PPW conjecture in curved spaces

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• 作者：Nick Edelen ^{nedelen@mit.edu}
• 关键词：Isoperimetric ; Eigenvalue ; Inequality ; Negative curvature
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：272
• 期：3
• 页码：849-865
• 全文大小：330 K
• 卷排序：272

文摘

In Euclidean ([1]) and Hyperbolic ([5]) space, and the round hemisphere ([2]), geodesic balls maximize the gap λ2−λ1λ2−λ1 of Dirichlet eigenvalues, among domains with fixed λ1λ1. We prove an upper bound on λ2−λ1λ2−λ1 for domains in manifolds with certain curvature bounds. The inequality is sharp on geodesic balls in spaceforms.