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NCTS Differential Geometry Seminar
 
21:30 - 22:30, March 8, 2023 (Wednesday)
Cisco Webex, Online seminar
(線上演講 Cisco Webex)
Area Ratio Bounds and the Existence of Anisotropic Minimal Surfaces
Yangyang Li (The University of Chicago)

Abstract

Anisotropic area, a generalization of the area functional, arises naturally in models of crystal surfaces. Due to the lack of a monotonicity formula, the regularity theory for its critical points, anisotropic minimal surfaces, is much 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 min-max construction. This 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.
 
Meeting number (access code): 2511 626 6343
Meeting password: YJtA2ycrY32


 

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