On the fundamental tone of minimal submanifolds with controlled extrinsic curvature
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comunitat-uji-handle2:10234/7037
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Title
On the fundamental tone of minimal submanifolds with controlled extrinsic curvatureAuthor (s)
Date
2013Publisher
SpringerISSN
0926-2601; 1572-929XType
info:eu-repo/semantics/articlePublisher version
https://link.springer.com/article/10.1007%2Fs11118-013-9349-6Version
info:eu-repo/semantics/acceptedVersionSubject
Abstract
The aim of this paper is to obtain the fundamental tone for minimal submanifolds of the Euclidean or hyperbolic space under certain restrictions on the extrinsic curvature. We show some sufficient conditions on the ... [+]
The aim of this paper is to obtain the fundamental tone for minimal submanifolds of the Euclidean or hyperbolic space under certain restrictions on the extrinsic curvature. We show some sufficient conditions on the norm of the second fundamental form that allow us to obtain the same upper and lower bound for the fundamental tone of minimal submanifolds in a Cartan–Hadamard ambient manifold. As an intrinsic result, we obtain a sufficient condition on the volume growth of a Cartan–Hadamard manifold to achieve the lowest bound for the fundamental tone given by McKean. [-]
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Potential Analysis, 2013, published online 07 JuneRights
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info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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- MAT_Articles [763]