A lower bound for the nodal sets of Steklov eigenfunctions

Xing Wang; Jiuyi Zhu

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arXiv · 1411.0708

A lower bound for the nodal sets of Steklov eigenfunctions

Xing Wang·Jiuyi Zhu

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Abstract

We consider the lower bound of nodal sets of Steklov eigenfunctions on smooth Riemannian manifolds with boundary--the eigenfunctions of the Dirichlet-to-Neumann map. Let $N_\lambda$ be its nodal set. Assume that zero is a regular value of Steklov eigenfunctions. We show that $$H^{n-1}(N_\lambda)\geq C\lambda^{\frac{3-n}{2}}$$ for some positive constant $C$ depending only on the manifold.

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Xing Wang, Jiuyi Zhu. 2014-11-03. A lower bound for the nodal sets of Steklov eigenfunctions. https://arxiv.org/abs/1411.0708

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