On the Convergence Behavior of Conformal Immersion Sequence from Cylinders  

作　　者：Li CHEN 

机构地区：[1]School of Mathematics and Statistics, Hubei University

出　　处：《Acta Mathematica Sinica,English Series》2014年第6期1050-1060,共11页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.11201131)

摘　　要：In this paper, we are concerned with the convergence behavior of a sequence of conformal immersions {fn} from long cylinders Pn with Pn｜Afn｜2＋ μ（fn（Pn）） 〈 Λ. We show that if {fn} does not converge to a point, the total Gauss curvatures and the measures of the images of {fn} will not lose on the necks and each neck consists of a point.In this paper, we are concerned with the convergence behavior of a sequence of conformal immersions {fn} from long cylinders Pn with Pn｜Afn｜2＋ μ（fn（Pn）） 〈 Λ. We show that if {fn} does not converge to a point, the total Gauss curvatures and the measures of the images of {fn} will not lose on the necks and each neck consists of a point.

关 键 词：Conformal immersion blow up the second fundament form 

分 类 号：O186.11[理学—数学]