Vishnu Nandakumaran (Notre Dame)

Title: Minimal surfaces near Hardt-Simon foliations

Abstract: Caffarelli-Hardt-Simon used the minimal surface equation on the Simons cone to generate newer examples of minimal hypersurfaces with isolated singularities. Hardt-Simon proved that every area-minimizing quadratic cone having only an isolated singularity can be approximated by a unique foliation of smooth, area-minimizing hypersurfaces asymptotic to the quadratic cone. In this talk, we shall discuss a recent result where we solve the minimal surface equation on Hardt-Simon foliations. We use glueing methods to construct minimal surfaces near quadratic cones and study a Dirichlet-type problem near quadratic cones.