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Geometric Analysis Seminar

Topological control for min-max free boundary minimal surfaces

Giada Franz (MIT)

Location:  Hill-705
Date & time: Tuesday, 26 September 2023 at 2:50PM - 3:50PM

Abstract: A free boundary minimal surface (FBMS) in a three-dimensional Riemannian manifold is a critical point of the area functional with respect to variations that constrain its boundary to the boundary of the ambient manifold. A very natural question is the one of constructing FBMS (in a given ambient manifold) of a given topological type.  In this talk, we will focus on one of the methods that have been employed so far to tackle this problem, that is Simon-Smith variant of Almgren-Pitts min-max theory.   We will see how this method allows us to control the topology (i.e. genus and number of boundary components) of the resulting surface, and we will present several applications.   Based on joint work with Mario Schulz.

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