Speaker: Chen-Kuan Lee
University of Notre Dame
Will give a Graduate Student Geometry Seminar entitled:
Perturbations of a minimal surface with triple junctions in $\mathbb{R}^2 \times \mathbb{S}^1$
Abstract: Surfaces with triple junctions arise naturally in the study of minimal surfaces in Euclidean space. Taylor showed that there are only two possible singularities of certain almost-area-minimizing surfaces. One of them is the triple junctions, which consists of three surfaces that meet at $120^\circ$. In this talk, we construct examples of minimal surfaces with a circle of triple junctions modeled on $\mathbf{Y} \times \mathbb{S}^1$ in $\mathbb{R}^2 \times \mathbb{S}^1$. Given any (small) perturbations of the boundary circles $(\mathbf{Y} \times \mathbb{S}^1) \cap \partial \mathbf{B}$, where $\mathbf{B} = B_1^2(0) \times \mathbb{S}^1$ is the solid torus in $\mathbb{R}^2 \times \mathbb{S}^1$, we shall find perturbations of $(\mathbf{Y} \times \mathbb{S}^1) \cap \mathbf{B}$ which are stationary and have the prescribed boundary.
Date: 03-07-2025
Time: 4:00 pm
Location: 258 Hurley Bldg