On the Gauss Curvature of Minimal Surfaces

摘要

The majority of results in this paper are derived from the following observation. Given a point p on a minimal surface, one may assign to each point of a suitable neighborhood N of p two complex variables £ and w, such that the correspondence between £ and w is analytic, and for the Gauss curvature K at each point of N we have the formulanThis allows us to translate elementary properties of analytic functions into geometric statements about minimal surfaces.