Conformal Maps And Geometry

Introduction

'I very much enjoyed reading this book ... Each chapter comes with well thought-out exercises, solutions to which are given at the end of the chapter. Conformal Maps and Geometry presents key topics in geometric function theory and the theory of univalent functions, and also prepares the reader to progress to study the SLE. It succeeds admirably on both counts.'

Overview

MathSciNet

Topics Covered

Geometric function theory is one of the most interesting parts of complex analysis, an area that has become increasingly relevant as a key feature in the theory of Schramm-Loewner evolution.

Context

Though Riemann mapping theorem is frequently explored, there are few texts that discuss general theory of univalent maps, conformal invariants, and Loewner evolution. This textbook provides an accessible foundation of the theory of conformal maps and their connections with geometry.

Unique Aspects

It offers a unique view of the field, as it is one of the first to discuss general theory of univalent maps at a graduate level, while introducing more complex theories of conformal invariants and extremal lengths.

Target Audience

Conformal Maps and Geometry is an ideal resource for graduate courses in Complex Analysis or as an analytic prerequisite to study the theory of Schramm-Loewner evolution.