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Geometry and interior nodal sets of Steklov eigenfunctions

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arxiv 1510.07300 v4 pith:7G2MXSKS submitted 2015-10-25 math.AP math.SP

Jiuyi Zhu This is my paper · ORCID
classification math.APmath.SP
keywords eigenfunctionsinteriormanifoldsnodalsetssteklovableanalytic
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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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  1. Domains without dense Steklov nodal sets

    math.AP 2019-08 accept novelty 8.0 of 10

    For a dense family of analytic planar domains, Steklov eigenfunctions have fixed-size zero-free balls in the interior, so their nodal sets are not dense at any shrinking scale.

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