The Dirac operator on untrapped surfaces

Details The Dirac operator on untrapped surfaces The Dirac operator on untrapped surfaces

2011-10-15

arxiv.org/abs/1110.3395v1

Mathematics

Differential Geometry

16 pages

Scientific paper

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.

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