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),w...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.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11271378,11071179 and 10871211)
文摘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.
