16:15 Uhr | Mattias Dahl (KTH Stockholm) | An initial data version of topological censorship in higher dimensions
The principle of topological censorship states that the region outside
all black holes in a spacetime should be topologically simple. Classical
results show for example that this region is simply connected in 3+1
dimensions.
Recently, an initial data version of topological censorship has been
found by
Eichmair, Galloway, and Pollack. This states that for a 3-dimensional
asymptotically flat initial data set for general relativity the domain
outside the outermost marginally trapped surface is diffeomorphic to
Euclidean space minus a number of balls.
In this talk I will describe another approach to the initial data
version of topological censorship which gives constraints on the
topology also in higher dimensions. This is joint work with L.
Andersson, G. Galloway, and D. Pollack.
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17:45 Uhr | Kirk Lancaster (Wichita State University) | Boundary Behavior of PMC Surfaces: The Concus-Finn Conjecture
Capillary surfaces are interesting geometric objects which turn out to be
important in microgravity environments (e.g. in space) and in tiny devices
(e.g. electronic, "lab on a chip"). This talk will focus on the mathematical
theory of capillary surfaces in vertical cylinders and sketch the proof of
the Concus-Finn conjecture. Related open questions will be mentioned.
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