DMS Topology Seminar

Speaker: Brian Freidin 

Title: Free boundary minimal surfaces in the ball

Abstract: Minimal surfaces are critical points for the area function on the space of submanifolds, say of R^n. In a bounded region V the free boundary problem asks for critical points of the area function on the space of submanifolds with boundary contained in the boundary of V. We will survey some results about what topologies can occur (classified by genus and number of boundary components in dimension 2) for free boundary minimal surfaces in the ball. Then we will discuss a construction for such surfaces by searching in the lower-dimensional space of G-invariant surfaces, for various groups G.