A CONCAVITY CONDITION FOR EXISTENCE OF A NEGATIVE VALUE IN NEUMANN-POINCARE SPECTRUM IN THREE DIMENSIONS
A CONCAVITY CONDITION FOR EXISTENCE OF A NEGATIVE VALUE IN NEUMANN-POINCARE SPECTRUM IN THREE DIMENSIONS
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DOI：
10.1090/proc/14467
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发表时间：
2019-08-01
影响因子：
1
通讯作者：
Kang, Hyeonbae
中科院分区：
文献类型：
--
作者：
Ji, Yong-Gwan;Kang, Hyeonbae
证明了如果三维有界区域满足一定的边界条件，则该区域边界上的Neumann-Poincare算子或其在球面上的逆算子在其谱中有负值.这个条件很简单，如果边界上有一个点的高斯曲率为负，则满足这个条件。
It is proved that if a bounded domain in three dimensions satisfies a certain concavity condition, then the Neumann-Poincare operator on either the boundary of the domain or its inversion in a sphere has a negative value in its spectrum. The concavity condition is quite simple, and is satisfied if there is a point on the boundary at which the Gaussian curvature is negative.