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Geometry of infinite-dimensional Teichmuller spaces

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【作者】 李忠；

【Author】 LI Zhong(Department of Mathematics, Peking University, Beijing 100871, China)

【机构】 Department of Mathematics； Peking University； Beijing 100871； China；

【摘要】 <正> The purpose of this paper is to survey the new advances in the research on the metric geometry of infinne-dimenstonal Tetchmuller spaces in recent years. It contains the following problems and their solutions: the non-umqueness of geodesic segments; the relation between the uniqueness of segments and the uniqueness of extremal Bel-trarni differentials; non-convexity of spheres and non-differentiability of the Teichmuller metric; isometrically embed-ded polydisks; Busernann points and Strebel points, and their equivalence.

【Abstract】 The purpose of this paper is to survey the new advances in the research on the metric geometry of infinne-dimenstonal Tetchmuller spaces in recent years. It contains the following problems and their solutions: the non-umqueness of geodesic segments; the relation between the uniqueness of segments and the uniqueness of extremal Bel-trarni differentials; non-convexity of spheres and non-differentiability of the Teichmuller metric; isometrically embed-ded polydisks; Busernann points and Strebel points, and their equivalence.

【关键词】 Riemann surfaces； Teichmuller spaces； quasiconfonnal mappings； Busemann geometry of geodesies.；
【Key words】 Riemann surfaces； Teichmuller spaces； quasiconfonnal mappings； Busemann geometry of geodesies.；
【基金】 Project supported in part by the National Natural Science Foundation of China (Grant No. 19136006) and the Doctoral Ld(?)tion Program Foundation of the State Education Commission of China.
  • 【文献出处】 Progress in Natural Science ,自然科学进展(英文版) , 编辑部邮箱 ,1999年05期
  • 【分类号】O182
  • 【下载频次】30
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