Quasiconformal Teichmuller Theory
Author | : Frederick P. Gardiner |
Publisher | : American Mathematical Soc. |
Total Pages | : 396 |
Release | : 2000 |
ISBN-10 | : 9780821819838 |
ISBN-13 | : 0821819836 |
Rating | : 4/5 (38 Downloads) |
Book excerpt: The Teichmüller space T(X) is the space of marked conformal structures on a given quasiconformal surface X. This volume uses quasiconformal mapping to give a unified and up-to-date treatment of T(X). Emphasis is placed on parts of the theory applicable to noncompact surfaces and to surfaces possibly of infinite analytic type. The book provides a treatment of deformations of complex structures on infinite Riemann surfaces and gives background for further research in many areas. These include applications to fractal geometry, to three-dimensional manifolds through its relationship to Kleinian groups, and to one-dimensional dynamics through its relationship to quasisymmetric mappings. Many research problems in the application of function theory to geometry and dynamics are suggested.