Existence and regularity of anisotropic minimal hypersurfaces
Dr. Yangyang Li
2023-06-20 9:00-10:00
MCM110&Online
Speaker: Dr. Yangyang Li (Chicago University)Time: 9:00-10:00 June 20, 2023 (Tuesday)
Place: MCM110 & Online (Zoom ID: 3329836068 Password: mcm1234)
Title: Existence and regularity of anisotropic minimal hypersurfaces
Abstract: Anisotropic area, a generalization of the area functional, arises naturally in models of crystal surfaces. Due to the absence of a monotonicity formula, the regularity theory for its critical points, anisotropic minimal surfaces, is significantly more challenging than the area functional case. In this talk, I will discuss how one can overcome this difficulty and obtain a smooth anisotropic minimal surface for elliptic integrands in closed 3-dimensional Riemannian manifolds via a min-max construction. This result confirms a conjecture by Allard [Invent. Math.,1983] in dimension 3. The talk is based on joint work with Guido De Philippis and Antonio De Rosa.
