Back to Departmental Colloquium: Spring 2011
Departmental Colloquium
Date: Thursday, Apr 14, 2011
Time: 4:15PM
Location: JWB 335
Jaigyoung Choe
Korean Institute for Advanced Study, visiting Stanford University
Title |
First eigenvalue of the Laplacian on a minimal surface in S3 |
Abstract |
A minimal surface is locally the surface with minimum area. Therefore the Euclidean coordinates $x_1,x_2,x_3$ are harmonic on a minimal surface in $\mathbb R^3$. And the Euclidean coordinates $x_i (i=1,2,3,4)$ satisfy $\Delta x_i+2x_i=0$ on a minimal surface in $\mathbb S^3(\subset\mathbb R^4)$. Then Yau conjectured that the first eigenvalue of the Laplacian on a compact embedded minimal surface in $\mathbb S^3$ should be just 2. In this talk I will first show how minimal surfaces are constructed in $\mathbb S^3$, and give an easy proof of Yau’s conjecture for most of the minimal surfaces. (Joint work with M. Soret) |
Applied Mathematics