OSU Mathematics Seminars and Colloquia
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Tue, Apr 26, 2022
Analysis Seminar
4:20 PM
MSCS 509
Gauss-Bonnet on asymptotically hyperbolic Einstein half-spaces
Stephen McKeown, UT Dallas
Host: Sean Curry
[Abstract] [PDF]
Abstract: First, we state a conformal Gauss-Bonnet theorem for four-manifolds with corner. Then we review the definition of the renormalized volume of asymptotically hyperbolic Einstein metrics, which came from the AdS/CFT correspondence in physics; and review the Gauss-Bonnet theorem for such manifolds in the ordinary case. We then state a new Gauss-Bonnet formula for half of an asymptotically hyperbolic Einstein space that has been partitioned into two by a minimal surface, and use this to derive a variation formula for its renormalized volume under variations of the minimal surface. The latter two results are joint work with Matthew J. Gursky and Aaron J. Tyrrell.
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