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

Yong-Gwan Ji; Hyeonbae Kang

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arXiv · 1808.10621

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

Yong-Gwan Ji·Hyeonbae Kang

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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.

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BibTeX RIS

Yong-Gwan Ji, Hyeonbae Kang. 2018-10-28. A concavity condition for existence of a negative Neumann-Poincaré eigenvalue in three dimensions. https://arxiv.org/abs/1808.10621

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