Compensated compactness and isometric embedding

Series: 
School of Mathematics Colloquium
Thursday, April 2, 2009 - 11:00
1 hour (actually 50 minutes)
Location: 
Skiles 269
,  
Department of Mathematics, University of Wisconsin
In this talk I will outline recent results of G-Q Chen, Dehua Wang, and me on the problem of isometric embedding a two dimensional Riemannian manifold with negative Gauss curvature into three dimensional Euclidean space. Remarkably there is very pretty duality between this problem and the equations of steady 2-D gas dynamics. Compensated compactness (L.Tartar and F.Murat) yields proof of existence of solutions to an initial value problem when the prescribed metric is the one associated with the catenoid.