The Dirac operator on untrapped surfaces
Differential Geometry
2014-05-28 v1
Abstract
We establish a sharp extrinsic lower bound for the first eigenvalue of the Dirac operator of an untrapped surface in initial data sets without apparent horizon in terms of the norm of its mean curvature vector. The equality case leads to rigidity results for the constraint equations with spherical boundary as well as uniqueness results for constant mean curvature surfaces in Minkowski space.
Cite
@article{arxiv.1110.3395,
title = {The Dirac operator on untrapped surfaces},
author = {Simon Raulot},
journal= {arXiv preprint arXiv:1110.3395},
year = {2014}
}
Comments
16 pages