A concavity condition for existence of a negative Neumann-Poincaré eigenvalue in three dimensions

It is proved that if a bounded domain in three dimensions satisfies a certain concavity condition, then the Neumann-Poincaré operator on the boundary of the domain or its inversion in a sphere has at least one negative eigenvalue. The concavity condition is quite simple, and is satisfied if there is...

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Bibliographic Details
Published in:arXiv.org 2018-10
Main Authors: Yong-Gwan Ji, Kang, Hyeonbae
Format: Article
Language:English
Subjects:
Concavity
Curvature
Eigenvalues
Online Access:Get full text
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Summary:It is proved that if a bounded domain in three dimensions satisfies a certain concavity condition, then the Neumann-Poincaré operator on the boundary of the domain or its inversion in a sphere has at least one negative eigenvalue. The concavity condition is quite simple, and is satisfied if there is a point on the boundary at which the Gaussian curvature is negative.
ISSN:2331-8422