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Brand new. We distribute directly for the publisher. The Teichmller space $T(X)$ is the space of marked conformal structures on a given quasiconformal surface $X$. This volume
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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.
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More About This Textbook
Overview
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.
Editorial Reviews
Booknews
Teichm<:u>ller space is a universal classification space for complex structures on a surface of given quasiconformal type. Gardiner and Lakic provide background for applying the underlying theory to dynamical systems, particularly to the iteration of rational maps and conformal dynamics to Kleinian groups and three-dimensional manifolds, to Fuchsian groups and Riemann surfaces, and to one-dimensional dynamics. They point out that though the theory is two-dimensional, it impinges on three-dimensional topology through its relationship to Kleinian groups and on one-dimensional dynamics through the quasi- symmetric boundary action of a quasiconformal self-map of a disc. Annotation c. Book News, Inc., Portland, OR (booknews.com)Product Details
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