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Abelian Teichmüller disks restricted by behavior 米谷, 文男 MAITANI, Fumio open access Riemann surface quasiconformal mapping Beltrami differential Teichmüller disk Torelli's theorem We shall investigate quasiconformal deformations of arbitrary Riemann surfaces whose Riemannian metrics are given by Beltrami differentials with complex parameters in the unit disk, where the Beltrami differentials are represented by certain holomorphic differentials with restricted boundary behavior. They are so called Abelian Teichmüller disks. For the sake of discussion on general open Riemann surfaces, we consider two types of boundary behavior. The one is based on Dirichlet finite harmonic differentials with integral periods and the other is based on holomorphic differentials with normal behavior. By using the arguments of F.Gardiner and I.Kra on punctured Riemann surfaces, we shall discuss extremal quasiconformal mappings in Torelli space, variational formulas of the norms of our restricted holomorphic differentials and Torelli's theorem on our Abelian Teichmüller disks of an arbitrary Riemann surface. Reprinted from the Memoirs of the Faculty of Engineering and Design, Kyoto Institute of Technology, Series of Science and Technology, Vol.35 (1986) pp.1-11 Submitted by 附属図書館 KIT-Repository (dspace-admin@jim.kit.ac.jp) on 2009-04-07T07:01:48Z No. of bitstreams: 1 maitani-1986.pdf: 535259 bytes, checksum: 7745eb9833c65579e181c58ee66f3d29 (MD5) Made available in DSpace on 2009-04-07T07:01:48Z (GMT). No. of bitstreams: 1 maitani-1986.pdf: 535259 bytes, checksum: 7745eb9833c65579e181c58ee66f3d29 (MD5) Previous issue date: 1987-03 1987-03 eng journal article VoR http://hdl.handle.net/10212/1906 https://kit.repo.nii.ac.jp/records/2000738 Reprinted from the Memoirs of the Faculty of Engineering and Design, Kyoto Institute of Technology, Series of Science and Technology 35 1 11 https://kit.repo.nii.ac.jp/record/2000738/files/maitani-1986.pdf application/pdf 522.7 KB