Ailana Fraser (University of British Columbia)

02/11 at 04:30 pm (CET)  

Free boundary minimal surfaces in rectangular prisms

In this talk we will describe recent work using eigenvalue optimization to construct free boundary minimal surfaces in products of Euclidean balls. We will briefly outline the general theory and apply it in a specific case to explain and generalize the Schwarz P-surface, which is a free boundary minimal surface in the three dimensional cube with one boundary component on each face of the cube. We will show how the method can be used to construct such surfaces in rectangular prisms with arbitrary side lengths. We will also show that when the side lengths are not all the same, there are at least two minimal surfaces of the type of the Schwarz P-surface and both are embedded.

Javier Gómez-Serrano (Brown University)

30/11 at 4:30 pm (CET)  

Valentino Tosatti (NYU Courant)

11/12 at 4:30 pm (CET) 

Robin Neumayer (Carnegie Mellon University)

14/12 at 4:30 pm (CET) 

Tatsuya Miura (Kyoto University)

25/01 at 11:30 am (CET) 

Simon Brendle (Columbia)

28/09 at 4:30 pm (CEST)

A dimension descent scheme for the positive mass theorem in arbitrary dimension

We describe an inductive scheme for proving the positive mass theorem in arbitrary dimension, extending the minimal hypersurface approach pioneered by Schoen and Yau. This is joint work with Yipeng Wang.

Christos Mantoulidis (Rice University) 

06/10 at 4:30 pm (CEST)

 Generic perturbations of mean curvature flows

I will discuss work with O. Chodosh, K. Choi, and F. Schulze on perturbations of mean curvature flows in R^3, near multiplicity-one non-generic singular points, which avoid non-generic singularities. This is our most succinct parabolic analogue for Hardt--Simon's well-known generic regularity theorem for the elliptic area-minimization problem.

William P. Minicozzi II (MIT)

26/10 at 4:30 pm (CET)  

Distance between minimal surfaces and flow

The distance between two minimal hypersurfaces is a Lipschitz continuous supersolution, in the viscosity sense, of a natural elliptic partial differential equation. This gives a new perspective on several well-known global properties of minimal hypersurfaces and also encodes richer local information.  I will also cover a generalization to mean curvature flow. This is joint work with Toby Colding.