体积约束下的大斯特克洛夫特征值

Alexandre Girouard, Panagiotis Polymerakis
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引用次数: 0

摘要

在本论文中,我们用漂移拉普拉斯的辅助斯特克洛夫问题建立了翘曲积的斯特克洛夫谱表达式,漂移拉普拉斯的权重由翘曲因子引起。作为应用,我们证明了一个具有与积相差形的连通边界的紧凑流形存在一族黎曼度量,它们在边界上重合,具有固定的体积和任意大的第一个非零斯特克洛夫特征值。这是三维流形上具有这些性质的黎曼度量的第一个例子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Large Steklov Eigenvalues Under Volume Constraints

In this note we establish an expression for the Steklov spectrum of warped products in terms of auxiliary Steklov problems for drift Laplacians with weight induced by the warping factor. As an application, we show that a compact manifold with connected boundary diffeomorphic to a product admits a family of Riemannian metrics which coincide on the boundary, have fixed volume and arbitrarily large first non-zero Steklov eigenvalue. These are the first examples of Riemannian metrics with these properties on three-dimensional manifolds.

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