The theory of Riemann surfaces has a geometric and an analytic part. The former deals with the axiomatic definition of a Riemann surface, methods of construction, topological equivalence, and conformal mappings of one Riemann surface on another. The analytic part is concerned with the existence and properties of functions that have a special character connected with the conformal structure, for instance: subharmonic, harmonic, and analytic functions.
Originally published in 1960.
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Table of Contents:
- Frontmatter, pg. i
- Preface, pg. v
- Contents, pg. vii
- Chapter I. Surface Topology, pg. 1
- Chapter II. Riemann Surfaces, pg. 112
- Chapter III. Harmonic Functions on Riemann Surfaces, pg. 148
- Chapter IV. Classification Theory, pg. 196
- Chapter V. Differentials on Riemann Surfaces, pg. 265
- Bibliography, pg. 332
- Index, pg. 374
Other Princeton books authored or coauthored by Lars Valerian Ahlfors:
Another Princeton book authored or coauthored by Leo Sario: