Sharp upper bound and a comparison theorem for the first nonzero Steklov eigenvalue

In this paper we prove that given a volume, among all domains with smooth boundary in rank-1 symmetric spaces of noncompact type, geodesic balls maximizes the first nonzero Steklov eigenvalue. We also prove a comparison result for the first nonzero Steklov eigenvalue for domains in simply connected...

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Hauptverfasser: Binoy, Santhanam, G
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Sprache:eng
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Zusammenfassung:In this paper we prove that given a volume, among all domains with smooth boundary in rank-1 symmetric spaces of noncompact type, geodesic balls maximizes the first nonzero Steklov eigenvalue. We also prove a comparison result for the first nonzero Steklov eigenvalue for domains in simply connected Riemannian manifolds with certain curvature bounds.
DOI:10.48550/arxiv.1208.1690