Spectral Bounds for Dirac Operators on Open Manifolds

TL;DR

This paper extends classical eigenvalue bounds for Dirac operators from compact to noncompact, possibly incomplete manifolds, broadening the applicability of these estimates in geometric analysis.

Contribution

It generalizes well-known eigenvalue estimates for Dirac operators to noncompact and incomplete manifolds, including Friedrich's estimate and a surface estimate.

Findings

Extended Friedrich's estimate to noncompact manifolds

Generalized eigenvalue bounds to incomplete surfaces

Broadened the scope of spectral estimates in geometric analysis

Abstract

We extend several classical eigenvalue estimates for Dirac operators on compact manifolds to noncompact, even incomplete manifolds. This includes Friedrich's estimate for manifolds with positive scalar curvature as well as the author's estimate on surfaces.