Conformal Mappings of Surfaces and Cauchy-Riemann Inequalities.

摘要

H. Hopf has introduced the use of holomorphic quadratic forms to study surfaces with constant mean curvature in R/sup 3/. The same techniques have been used to study surfaces immersed in spaces forms, complex projective spaces and also to study harmonic maps. Following Hopf's ideas we consider holomorphic type forms, that is, forms whose zeroes behave like zeroes of holomorphic forms, to study surfaces such that the norm of the mean curvature vector or of its covariant derivative satisfies some inequality. We also apply the same techniques to study maps whose tension field satisfies similar property. (author). 17 refs. (Atomindex citation 19:059903)