Rigidity on an eigenvalue problem with mixed boundary condition

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arxiv 1710.06701 v1 pith:DZ7TX423 submitted 2017-10-18 math.DG

Sergio Almaraz , Ezequiel Barbosa This is my paper · ORCID

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keywords boundaryconditioneigenvaluemixedproblemrigidityapplyobata-type

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We prove an Obata-type rigidity result for the spherical cap and apply it for an eigenvalue problem with mixed boundary condition.

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Some rigidity results related to the Obata type equation
math.DG 2024-11 conditional novelty 6.0 of 10

For the Obata-type equation with Robin boundary constant c>1 and suitable curvature bounds, the manifold is forced to be a geodesic ball in hyperbolic space, or a warped product over a standard sphere.