The Complex Analytic Theory of Teichmuller Spaces

Dealing with the complex analytic theory of Teichmuller spaces, this book concentrates on providing a self-contained development of the fundamental results regarding the complex structure of the Teichmuller moduli spaces of Reimann surfaces. The reader is shown how Teichmuller spaces embody a large group of concrete examples of complex manifolds (of finite and infinite dimension). Emphasis is placed on the Bers embedding of the Teichmuller spaces in Banach spaces of quadratic holomorphic differentials. String theory, which holds the promise of a complete "unified field theory", is also discussed. Written at a level that is accessible to both graduate students and experts, the book includes topics such as quasiconformal mappings, automorphic forms, Reimann surfaces and a proof of the universal property of Teichmuller spaces. An appendix on invarian spaces provides an introduction to the intrinsic differential geometry of the Teichmuller spaces.