Abstract. We present a method for constructing global holomorphic peak functions from local holomorphic support functions for broad classes of unbounded domains in C n . As an application, we establish a method for showing the positivity and completeness of invariant metrics including the Bergman metric mainly for the unbounded domains.
Abstract. We consider a finite composition of generalized Hénon mappings f : C 2 → C 2 and its Green function g + : C 2 → R ≥0 (see Section 2). It is well known that each level set {g + = c} for c > 0 is foliated by biholomorphic images of C and each leaf is dense. In this paper, we prove that each leaf is actually an injective Brody curve in P 2 (see Section 4). We also study the behavior of the level sets of g + near infinity.
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.