Measure of nodal sets of analytic Steklov eigenfunctions

Abstract

Let $(\Omega ,g)$ be a real analytic Riemannian manifold with real analytic boundary $\partial \Omega$. Let ${\psi }_{\lambda }$ be an eigenfunction of the Dirichlet-to-Neumann operator $\Lambda$ of $(\Omega ,g,\partial \Omega )$ of eigenvalue $\lambda$. Let ${\mathcal{N}}_{{\lambda }_j}$ be its nodal set. Then ${\mathcal{H}}^{n-2}({\mathcal{N}}_{\lambda })\le C_{g,\Omega }\lambda .$ This proves a conjecture of F. H. Lin and K. Bellova.

References in corpus (1)

• Nodal Sets of Steklov Eigenfunctions

Cited by in corpus (8)

• Geometry and interior nodal sets of Steklov eigenfunctions
• Nodal sets of Robin and Neumann eigenfunctions
• Upper bounds of nodal sets for eigenfunctions of eigenvalue problems
• Interior nodal sets of Steklov eigenfunctions on surfaces
• Lower bounds for interior nodal sets of Steklov eigenfunctions
• Doubling property and vanishing order of Steklov eigenfunctions
• Hausdorff measure bounds for nodal sets of Steklov eigenfunctions
• Doubling inequalities and critical sets of Dirichlet eigenfunctions