Submanifold geometry, nonlinear partial differential equations and Banach loop groups.

摘要

This dissertation deals with some geometric problems related to nonlinear partial differential equations like the sine-Gordon equation and the Korteweg-de Vries (KdV) equation and applications of these equations in differential geometry. What we are interested in are explicit relations among (1) Weingarten surfaces in R;The main ideas in our approach are as follows. Consider a class of submanifolds such as constant mean curvature surfaces in R