Quasiconformal Teichmuller Theory (Mathematical Surveys and Monographs)
Quasiconformal Teichmuller Theory (Mathematical Surveys and Monographs) by Frederick P. Gardiner
English | 1999 | ISBN: 0821819836 | 372 Pages | PDF | 36.70 MB
English | 1999 | ISBN: 0821819836 | 372 Pages | PDF | 36.70 MB
The Teichmuller 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.