CANCELLED - GAMP seminar by Mattias Dahl (KTH) – University of Copenhagen

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CANCELLED - GAMP seminar by Mattias Dahl (KTH)

CANCELLED - GAMP (Geometric Analysis and Mathematical Physics) Seminar.

Speaker: Mattias Dahl (KTH).

CANCELLED  Title: Outermost apparent horizons with non-trivial topology.

Abstract: An outermost apparent horizon in an asymptotically Euclidean manifold is a closed minimal hypersurface enclosing all other such hypersurfaces. In three dimensions, Hawking's black hole topology theorem states that an outermost apparent horizon must have a metric with positive scalar curvature if the surrounding manifold has non-negative scalar curvature. This has been generalized to higher dimensions by Cai, Galloway and Schoen.

It is conceivable that the existence of a positive scalar curvature metric is the only restriction on a bounding manifold to be an outermost apparent horizon. In this talk I want to describe some new metrics with outermost apparent horizons having non-trivial topology. These examples are constructed by a conformal blow up along a submanifold in Euclidean space, and the horizons are tubes around this submanifold. I will also discuss possible ways to go further and prove that all bounding manifolds with positive scalar curvature can be outermost horizons.

The results presented are from joint work with Eric Staffas.