Abstract by Mingyan Zhao
Resolving the gap for a free boundary on a cone
In this talk, I will show how a free boundary problem on a cone is analogous to distance-minimizing paths on a cone. We will also discuss what is known for two and three-dimensional cones. I will show how using computer-assisted proof we may completely close the gap for a free boundary problem on a three-dimensional cone by showing all stable solutions are indeed minimizers of the functional.