Daivde Parise will give the geometry seminar on 19th October at 1:30pm in the Salle des Profs (9th floor building NO). Note the unusual time: this is to be able to fit in two talks. The other speaker is Salammbo Connolly. Davide’s title is “Uniqueness of free-boundary minimal annuli” and his title is below.
A recurring theme in differential geometry is understanding when a set of geometric conditions uniquely characterizes an object. In this talk, I will discuss this question for minimal surfaces in the unit ball, focusing on those meeting the boundary orthogonally. I will explain recent joint work with Jonathan Zhu in which we prove that every properly embedded, free-boundary, minimal annulus is congruent to the critical catenoid. I will also describe closely related results for axially symmetric Alt-Caffarelli cones and free-boundary minimal annuli in spherical caps, and discuss connections with other uniqueness results in differential geometry.