On a free boundary problem and minimal surfaces
Yong Liu, Kelei Wang, Juncheng Wei · arXiv (Cornell University) · 2017
From minimal surfaces such as Simons' cone and catenoids, using refined Lyapunov-Schmidt reduction method, we construct new solutions for a free boundary problem whose free boundary has two components. In dimension $8$, using variational arguments, we also obtain solutions which are global minimizers of the corresponding energy functional. This shows that Savin's theorem is optimal.