Boundary Value Problems for Surfaces of Constant Gauss Curvature. (Reannouncementwith New Availability Information)

摘要

The compact smooth surfaces in cu R with constant positive Gauss curvature (K-surfaces) form a natural class. A K-surface without boundary is itself the boundary of a convex body, so it must be embedded. The surfaces of interest to us have non-empty boundary and so are not necessarily embedded. A fundamental question is this: given a collection gamma = (C sub 1...,C sub n) of Jordan curves in Cu R, what are the K-surfaces with boundary gamma for example, if gamma is a single Jordan curve with no inflection points, does gamma bound a K-surface