Upper bounds on the size of nodal sets for Gevrey and quasianalytic Riemannian manifolds

TL;DR

This paper establishes new polynomial upper bounds on the size of nodal sets for eigenfunctions on Riemannian manifolds with Gevrey or quasianalytic regularity, advancing understanding of eigenfunction behavior.

Contribution

It provides the first polynomial bounds for nodal set sizes in the context of Gevrey and quasianalytic manifolds, extending previous results beyond analytic cases.

Findings

Polynomial upper bounds for nodal sets on Gevrey manifolds

Extension of bounds to quasianalytic regularity

Improved understanding of eigenfunction nodal structures

Abstract

We find new polynomial upper bounds for the size of nodal sets of eigenfunctions when the Riemannian manifold has a Gevrey or quasianalytic regularity.