Conformal Dynamical Systems and Lipman Bers

The Expansion Theorem for Pseudo-analytic Functions1 Shmuel Agmon and Lipman Bers

On Rings of Analytic Functions

Let D be a domain in the complex plane (Riemann sphere) and R(D) the totality of one-valued regular analytic functions defined in D. With the usual definitions of addition and multiplication R(D) becomes a commutative ring (in fact, a domain of integrity). A oneto-one conformai transformation f =0(z) of D onto a domain A induces an isomorphism ƒ—>ƒ* between R(D) and R(A):f(z) =ƒ*[(2)]. An an...

Mathema Tics: L. Bers

An Outline of the Theory of Pseudoanalytic Functions

The Grafting Map of Teichmüller Space

1.1 Statement and Context. One of the underlying principles in the study of Kleinian groups is that aspects of the complex projective geometry of quotients of Ĉ by the groups reflect properties of the threedimensional hyperbolic geometry of the quotients of H by the groups. Yet, even though it has been over thirty-five years since Lipman Bers wrote down a holomorphic embedding of the Teichmülle...