On analytic and geometric properties of Teichmüller spaces
The work is devoted to application of methods of the geometric theory of functions to the theory of Teichmüller spaces. In the first part, the author develops and improves the results of \textit{I. V. Zhuravlev} [Sov. Math., Dokl. 21, 252-255 (1980); translation from Dokl. Akad. Nauk SSSR 250, 1047-1050 (1980; Zbl 0467.30037)]. The obtained results are used for a new proof of the theorem of \textit{W. Abikoff} [Ann. Math. Stud. 97, 3-5 (1981; Zbl 0458.30031)] on the structure of the boundary of a Teichmüller space, a new proof of the results of \textit{S. L. Krushkal'} [Sov. Math., Dokl. 17, 704-707 (1976); translation from Dokl. Akad. Nauk SSSR 228, 290-292 (1976; Zbl 0347.32011)] and these of \textit{I. Kra} [Lect. Notes Math. 747, 230-241 (1979; Zbl 0422.32018)] on completeness of the Teichmüller metric. The second part of the work is devoted to the study of boundary behaviour of holomorphic mappings of a unit disc into the Teichmüller space. In the third part, the boundary behaviour of the first kind holomorphic differentials as functions on the Teichmüller space are studied.
boundary behaviour of holomorphic mappings
scientific article; zbMATH DE number 3948731