Event Detail

Event Type: 
Department Colloquium
Monday, February 10, 2020 - 16:00 to 16:50
Kidder Hall 364

Speaker Info

Brigham Young University

Geometric measure theory and the study of free boundary problems in PDE share many methods and techniques. Indeed, the one phase free boundary problem shares a well-known connection to area-minimizing surfaces. In this talk we review this connection and explain how many results for area minimizing surfaces have analogous results for the one-phase free boundary problem. I will then discuss recent results for the one-phase problem on cones. After reviewing results of the author with H. Chang Lara on two-dimensional cones, we revisit the connection to area-minimizing surfaces to gain insight into the problem on higher dimensional cones. We then present new results on when the free boundary is allowed to pass through the vertex of a three-dimensional cone as well as results for higher dimensional cones.