Alejandro Penuela – Potsdam University
Date/Time/Location
Thursday, September 28th, 12:00pm; Hill Center 705
Local foliations by critical surfaces of the Hawking energy and the small sphere limit
The Hawking energy is one of the most famous quasi-local energies in general relativity. By using a Lyapunov-Schmidt reduction procedure we construct close to a point unique local foliations of critical surfaces of the Hawking energy on initial data sets (spacelike hypersurfaces in a spacetime), and we show a nonexistence condition. Any quasi-local energy should satisfy the so-called small sphere limit, therefore we also discuss the relation of these surfaces and the small sphere limit. In particular we discuss some discrepancies on the small sphere limit, when approaching a point with these foliations and when approaching as in the small sphere limit.