Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Dr. Yangyang Li，Chicago University
Inviter:
Title:	Existence and regularity of anisotropic minimal hypersurfaces
Language:	Chinese
Time & Venue:	2023.06.20 09:00-10:00 MCM110 Zoom ID: 3329836068 Password: mcm1234
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.