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# Mathematical Research Letters

## Volume 22 (2015)

### Number 4

### A lower bound for the nodal sets of Steklov eigenfunctions

Pages: 1243 – 1253

DOI: https://dx.doi.org/10.4310/MRL.2015.v22.n4.a14

#### Authors

#### 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

nodal sets, lower bound, Dirichlet-to-Neumann map, Steklov eigenfunctions

#### 2010 Mathematics Subject Classification

28A78, 35P15, 35R01, 58C40

Accepted 15 March 2015

Published 24 July 2015