Boundary value problems for noncompact boundaries of Spin$^c$ manifolds and spectral estimates
Differential Geometry
2017-05-17 v3 Spectral Theory
Abstract
We study boundary value problems for the Dirac operator on Riemannian Spin manifolds of bounded geometry and with noncompact boundary. This generalizes a part of the theory of boundary value problems by C. B\"ar and W. Ballmann for complete manifolds with closed boundary. As an application, we derive the lower bound of Hijazi-Montiel-Zhang, involving the mean curvature of the boundary, for the spectrum of the Dirac operator on the noncompact boundary of a Spin manifold. The limiting case is then studied and examples are then given.
Keywords
Cite
@article{arxiv.1207.4568,
title = {Boundary value problems for noncompact boundaries of Spin$^c$ manifolds and spectral estimates},
author = {Nadine Große and Roger Nakad},
journal= {arXiv preprint arXiv:1207.4568},
year = {2017}
}
Comments
Accepted in Proceedings of the London Mathematical Society