FALL 2020 Nonlinear Analysis Seminar Series

Professor Ulrich Menne
National Taiwan Normal University and National Center for Theoretical Sciences
 

Title: A priori geodesic diameter bounds for solutions to a variety of Plateau problems

Abstract:

Plateau's problem in Euclidean space may be given many distinct formulations with solutions to most of them admitting an associated varifold. This includes Reifenberg's approach based on sets and Čech homology as well as Federer and Fleming's approach using integral currents and their homology. Thus, we employ the setting of varifolds to prove a priori bounds on the geodesic diameter in terms of boundary behaviour. This is ongoing joint work with C. Scharrer.

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