Riemann Surfaces

  • Hershel M. Farkas
  • Irwin Kra

Part of the Graduate Texts in Mathematics book series (GTM, volume 71)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Hershel M. Farkas, Irwin Kra
    Pages 1-8
  3. Hershel M. Farkas, Irwin Kra
    Pages 9-29
  4. Hershel M. Farkas, Irwin Kra
    Pages 30-51
  5. Hershel M. Farkas, Irwin Kra
    Pages 52-150
  6. Hershel M. Farkas, Irwin Kra
    Pages 151-240
  7. Hershel M. Farkas, Irwin Kra
    Pages 241-279
  8. Hershel M. Farkas, Irwin Kra
    Pages 280-300
  9. Hershel M. Farkas, Irwin Kra
    Pages 301-329
  10. Back Matter
    Pages 330-340

About this book


The present volume is the culmination often years' work separately and joint­ ly. The idea of writing this book began with a set of notes for a course given by one of the authors in 1970-1971 at the Hebrew University. The notes were refined serveral times and used as the basic content of courses given sub­ sequently by each of the authors at the State University of New York at Stony Brook and the Hebrew University. In this book we present the theory of Riemann surfaces and its many dif­ ferent facets. We begin from the most elementary aspects and try to bring the reader up to the frontier of present-day research. We treat both open and closed surfaces in this book, but our main emphasis is on the compact case. In fact, Chapters III, V, VI, and VII deal exclusively with compact surfaces. Chapters I and II are preparatory, and Chapter IV deals with uniformization. All works on Riemann surfaces go back to the fundamental results of Rie­ mann, Jacobi, Abel, Weierstrass, etc. Our book is no exception. In addition to our debt to these mathematicians of a previous era, the present work has been influenced by many contemporary mathematicians.


Abelian variety Divisor Hilbert space Jacobi Riemann surface Riemannsche Fläche Surfaces Volume addition form holomorphic function integration theta function uniformization university

Authors and affiliations

  • Hershel M. Farkas
    • 1
  • Irwin Kra
    • 2
  1. 1.Department of MathematicsThe Hebrew University of JerusalemJerusalemIsrael
  2. 2.Department of MathematicsS.U.N.Y. at Stony BrookStony BrookUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York 1980
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-9932-2
  • Online ISBN 978-1-4684-9930-8
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site