CRM: Centro De Giorgi
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A Pisan workshop in Geometric Analysis

Equivariant min-max theory to construct free boundary minimal surfaces in the unit ball

speaker: Giada Franz (ETH Zurich)

abstract: A free boundary minimal surface (FBMS) in the three-dimensional Euclidean unit ball is a critical point of the area functional with respect to variations that constrain its boundary to the boundary of the ball (i.e. the unit sphere). A very natural question is whether there are FBMS in the unit ball of any given genus and number of boundary components. A powerful tool to construct minimal surfaces (both in the case without and with boundary) is the Almgren-Pitts min-max theory developed in the last 50 years. In this talk we present an equivariant version of this procedure and we use it to construct and study a new family of FBMS with connected boundary and any given genus in the unit ball.

Wed 13 Oct, 14:30 - 16:00, Aula Dini
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