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

Abstract

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.

References in corpus (2)

• The essential spectrum of the Neumann--Poincare operator on a domain with corners
• Weyl's law for the eigenvalues of the Neumann--Poincaré operators in three dimensions: Willmore energy and surface geometry

Cited by in corpus (3)

• Spectral structure of the Neumann--Poincaré operator on tori
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