Informal Geometric Analysis Seminar | Guoran Ye (Northwestern)

 Title: Regularity of Minimal Surfaces near Quadratic Cones

Abstract: I will be presenting Nick Edelen and Luca Spolaor's paper with the same name. Given a minimal cone C, for example, the Simons cone, what can we say about a minimal surface M "very close" to it? It turns out that M must be graphical over C or a smoothing S of C called the Hardt-Simon foliation. The key idea here is an analysis of the Jacobi operator and how its homogeneous terms of different orders correspond to explicit geometric operations.

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