Quasiconformal Teichmuller Theory

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.

Table of Contents

1. QUASICONFORMAL MAPPING

2. RIEMANN SURFACES

3. QUADRATIC DIFFERENTIALS, PART I

4. QUADRATIC DIFFERENTIALS, PART II

5. TEICHMULLER EQUIVALENCE

6. THE BERS EMBEDDING

7. KOBAYASHI’S METRIC ON TEICHMULLER SPACE

8. ISOMORPHISMS AND AUTOMORPHISMS

9. TEICHMULLER UNIQUENESS

10. THE MAPPING CLASS GROUP

11. JENKINS-STREBEL DIFFERENTIALS

12. MEASURED FOLIATIONS

13. OBSTACLE PROBLEMS

14. ASYMPTOTIC TEICHMULLER SPACE

15. ASYMPTOTICALLY EXTREMAL MAPS

16. UNIVERSAL TEICHMULLER SPACE

17. SUBSTANTIAL BOUNDARY POINTS

18. EARTHQUAKE MAPPINGS