Speaker: Luis Atzin Franco Reyna
University of Notre Dame
Will give a Graduate Student Geometry Seminar entitled:
Uniqueness of Tangent Cones for 2 Dimensional Minimizers
Abstract: In 1760 Lagrange raised Plateau’s problem, which roughly tries to find a surface that minimizes the area among surfaces with the same perimeter. This problem gave birth to an area of Geometric Analysis, Geometric Measure Theory. Herbert Federer and Wendell Fleming introduced the concept of area-minimizing currents, a generalization of minimal surfaces, to solve the problem in higher codimensions. This solved existence. Almost 30 years later, Sheldon Chang proved that in the case of 2-dimensional area-minimizing currents regularity is achieved and one obtains classical minimal surfaces. A key step in the proof was proving that tangent cones to 2d area-minimizing currents were unique, which was done by Brian White. In this talk, we will explain the relevance of tangent cones in the regularity theory and sketch the proof of the uniqueness of tangent cones to 2d area-minimizing currents.
Date: 10-11-2024
Time: 4:00 pm
Location: 258 Hurley Bldg
Originally published at math.nd.edu.