Differential Geometry Seminar

Bryan Christopher Dimler
Partial regularity for Lipschitz solutions to the minimal surface system


The minimal surface system is the Euler-Lagrange system for the area functional of a high codimension graph and reduces to the minimal surface equation in the case that the codimension is one. Though the regularity theory for the minimal surface equation is well understood, much less is known in the systems case. This is largely due to the examples provided by Lawson and Osserman in 1977 and the lack of a maximum principle for the system. In this talk, we discuss recent progress on the regularity theory for several notions of Lipschitz solutions to the minimal surface system with an emphasis on partial regularity results. These include stationary solutions, integral weak solutions, and viscosity solutions.

Event Date: 
February 29, 2024 - 11:30am to 12:30pm
Calendar Category: 
Seminar Category: 
Differential Geometry