Global solutions to the Gauss-Codazzi equations of isometric immersions

Dehua Wang
Department of Mathematics, University of Pittsburgh

Isometric immersion is an important problem in geometry. The Gauss-Codazzi equations for isometric immersions of surfaces will be considered. Various approaches and recent results on global solutions for the hyperbolic problem with negative Gauss curvatures will be presented. In particular, the global smooth isometric immersion of surfaces with slow decay rates for the curvatures will be discussed.