Boundary value problems for noncompact boundaries of Spin${}^c$ manifolds and spectral estimates

Abstract

We study boundary value problems for the Dirac operator on Riemannian Spin${}^c$ manifolds of bounded geometry and with noncompact boundary. This generalizes a part of the theory of boundary value problems by C. Bär 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${}^c$ manifold. The limiting case is then studied and examples are then given.

Accepted in Proceedings of the London Mathematical Society

References in corpus (2)

• The Energy-Momentum tensor on $Spi{n}^c$ manifolds
• The invertible double of elliptic operators

Cited by in corpus (6)

• Guide to Boundary Value Problems for Dirac-Type Operators
• Spacetime positive mass theorems for initial data sets with noncompact boundary
• Cauchy data spaces and Atiyah-Patodi-Singer index on non-compact manifolds
• The mass of an asymptotically hyperbolic end and distance estimates
• A generalized MIT Bag operator on spin manifolds in the non-relativistic limit
• First-order elliptic boundary value problems on manifolds with non-compact boundary