The Teichmuller space $T(X)$ is the space of marked conformal
structures on a given quasi conformal surface $X$. This volume uses
quasi conformal mapping to give a unified and up-to-date treatment
of $T(X)$. Emphasis is placed on parts of the theory applicable to
non compact 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 quasi symmetric mappings. Many research
problems in the application of function theory to geometry and
dynamics are suggested.
General
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