Geometry and interior nodal sets of Steklov eigenfunctions

Abstract

We investigate the geometric properties of Steklov eigenfunctions in smooth manifolds. We derive the refined doubling estimates and Bernstein's inequalities. For the real analytic manifolds, we are able to obtain the sharp upper bound for the measure of interior nodal sets.

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References in corpus (2)

• Measure of nodal sets of analytic Steklov eigenfunctions
• Spectral geometry of the Steklov problem

Cited by in corpus (2)

• Nodal sets of Robin and Neumann eigenfunctions
• Upper bounds of nodal sets for eigenfunctions of eigenvalue problems