An estimate on the nodal set of eigenspinors on closed surfaces

TL;DR

This paper develops a modified Bochner technique to relate the nodal set of eigenspinors to Dirac eigenvalues on closed surfaces, providing new inequalities and insights into spinorial solutions.

Contribution

It introduces a novel modified Bochner method to estimate the nodal set of eigenspinors, advancing understanding of spinorial eigenvalue problems on surfaces.

Findings

Derived an inequality linking nodal sets and eigenvalues

Applied technique to solutions of related spinorial equations

Provides bounds on nodal set measures

Abstract

We use a modified Bochner technique to derive an inequality relating the nodal set of eigenspinors to eigenvalues of the Dirac operator on closed surfaces. In addition, we apply this technique to solutions of similar spinorial equations.