A Remark on Recent Lower Bounds for Nodal Sets

Abstract

Recently, Sogge-Zelditch and Colding-Minicozzi gave new power law lower bounds on the size of the nodal sets of eigenfunctions. The purpose of this short note is to point out a third method to obtain a power law lower bound on the volume of the nodal sets. Our method is based on the Donnelly-Fefferman growth bound for eigenfunctions and a growth vs. volume relation we proved in a previous work.

4 pages; In section 2 an explanation of the basic iteration idea is added; acknowledgments added

References in corpus (2)

• Lower bounds for nodal sets of eigenfunctions
• Local Asymmetry and the Inner Radius of Nodal Domains

Cited by in corpus (2)

• Doubling inequality and nodal sets for solutions of bi-Laplace equations
• Lower bounds for nodal sets of Dirichlet and Neumann eigenfunctions