Convex hull of set in thick part of Teichmller space  

作　　者：LIU LiXin SHIGA Hiroshige SUN ZongLiang 

机构地区：[1]Department of Mathematics,Sun Yat-sen University [2]Department of Mathematics,Tokyo Institute of Technology [3]Department of Mathematics,Shenzhen University

出　　处：《Science China Mathematics》2014年第9期1799-1810,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11271378,11071179 and 10871211)

摘　　要：Let X be a non-elementary Riemann surface of type(g,n),where g is the number of genus and n is the number of punctures with 3g-3+n>1.Let T(X)be the Teichmller space of X.By constructing a certain subset E of T(X),we show that the convex hull of E with respect to the Teichmller metric,the Carathodory metric and the Weil-Petersson metric is not in any thick part of the Teichmler space,respectively.This implies that convex hulls of thick part of Teichmller space with respect to these metrics are not always in thick part of Teichmller space,as well as the facts that thick part of Teichmller space is not always convex with respect to these metrics.Let X be a non-elementary Riemann surface of type（g,n）,where g is the number of genus and n is the number of punctures with 3g-3＋n1.Let T（X）be the Teichmller space of X.By constructing a certain subset E of T（X）,we show that the convex hull of E with respect to the Teichmller metric,the Carathodory metric and the Weil-Petersson metric is not in any thick part of the Teichmler space,respectively.This implies that convex hulls of thick part of Teichmller space with respect to these metrics are not always in thick part of Teichmller space,as well as the facts that thick part of Teichmller space is not always convex with respect to these metrics.

关 键 词：Carathéodory metric Teichmuller metric Weil-Petersson metric convex hull Dehn twist 

分 类 号：O177[理学—数学]