A lower bound for the nodal sets of Steklov eigenfunctions

Xing Wang; Jiuyi Zhu

A lower bound for the nodal sets of Steklov eigenfunctions

Analysis of PDEs 2015-04-07 v2

Authors: Xing Wang , Jiuyi Zhu

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.

Keywords

Steklov eigenfunctions nodal sets lower bound Dirichlet-to-Neumann map Riemannian manifolds with boundary Hausdorff measure

Cite

@article{arxiv.1411.0708,
  title  = {A lower bound for the nodal sets of Steklov eigenfunctions},
  author = {Xing Wang and Jiuyi Zhu},
  journal= {arXiv preprint arXiv:1411.0708},
  year   = {2015}
}

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