Yau's Conjecture on the First Eigenvalue of the Laplacian on Minimal Surfaces in a sphere

Title Yau's Conjecture on the First Eigenvalue of the Laplacian on Minimal Surfaces in a sphere

 

SpeakerProf. Jaigyoung Choe (Korea Institute for Advanced Study, South Korea)

 

Time4:00-5:00 pm; March 28; 2013

 

PlaceConference Room A304, Department of Mathematical Sciences

 

Abstract: A minimal surface is locally the surface with minimum area. Therefore the Euclidean coordinates are harmonic on a minimal surface in Euclidean space. And the Euclidean coordinates are the eigenfunctions of eigenvalue 2 on a minimal surface in a sphere. Then Yau conjectured that the first eigenvalue of the Laplacian on a compact em-bedded minimal surface in a sphere should be just 2. In this talk I will give an easy proof of Yau's conjecture for the minimal surfaces constructed by Lawson and by Karcher-Pinkall-Sterling. (joint with M. Soret)

 

ContactHaizhong Li