Two applications of the Schwarz lemma
arXiv:1412.2680
Abstract
The Schwarz lemmas are well-known characterizations for holomorphic maps and we exhibit two examples of their applications. For a sequence family of biholomorphisms , it is useful to determine the location of for a fixed point in source manifolds (see Proposition \ref{2.5}). With it, we extend the Fornaess-Stout's theorem of \citep{FS77} in monotone unions of balls to ellipsoids in Section \ref{sec2}. In Section \ref{sec3}, we discuss the curvature bounds of complete Kähler metric on domains defined in \citep{Liu004} with an idea of \citep{Ya76}.