The equation for Gaussian curvature of a conformal metric is a special case of the classical differential equationwhere R c R*. We will use a technique introduced by Carleman to find restrictions on f and the set where a subharmonic function u can satisfy the above equation. This result will generate a relationship between the curvature and the metric of a nonpositively curved surface.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.