Lower bounds for nodal sets of eigenfunctions

TL;DR

This paper establishes lower bounds on the size of the zero sets of eigenfunctions, contributing to the understanding of their geometric properties.

Contribution

It provides new lower bounds for the Hausdorff measure of nodal sets of eigenfunctions, advancing theoretical knowledge in spectral geometry.

Findings

Lower bounds for Hausdorff measure of nodal sets

Quantitative estimates for eigenfunction zeros

Progress on conjectures in spectral geometry

Abstract

We prove lower bounds for the Hausdorff measure of nodal sets of eigenfunctions.