Picard-Type Theorem and Curvature Estimate on an Open Riemann Surface with Ramification  

作　　者：Zhixue LIU Yezhou LI 

机构地区：[1]School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China [2]Key Laboratory of Mathematics and Information Networks(Beijing University of Posts and Telecommunications),Ministry of Education,China

出　　处：《Chinese Annals of Mathematics,Series B》2023年第4期533-548,共16页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.12101068,12261106,12171050)。

摘　　要：Let M be an open Riemann surface and G:M→Pn(C)be a holomorphic map.Consider the conformal metric on M which is given by ds^(2)=‖■‖^(2m)|w|^(2),where■is a reduced representation of G,ωis a holomorphic 1-form on M and m is a positive integer.Assume that ds^(2) is complete and G is k-nondegenerate(0≤k≤n).If there are q hyperplanes H1,H2,…,Hq■Pn(C)located in general position such that G is ramified over Hj with multiplicity at leastγj(>k)for each j∈{1,2,…,q},and it holds that■,then M is flat,or equivalently,G is a constant map.Moreover,one further give a curvature estimate on M without assuming the completeness of the surface.

关 键 词：Picard-type theorem Holomorphic map Riemann surface Curvature estimate 

分 类 号：O186.11[理学—数学]