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Teichmüller Theory in Riemannian Geometry

  • Anthony J. Tromba

Part of the Lectures in Mathematics ETH Zürich book series (LM)

Table of contents

  1. Front Matter
    Pages ii-5
  2. Anthony J. Tromba
    Pages 6-13
  3. Anthony J. Tromba
    Pages 14-35
  4. Anthony J. Tromba
    Pages 36-62
  5. Anthony J. Tromba
    Pages 63-82
  6. Anthony J. Tromba
    Pages 83-95
  7. Anthony J. Tromba
    Pages 96-122
  8. Back Matter
    Pages 155-220

About this book

Introduction

These lecture notes are based on the joint work of the author and Arthur Fischer on Teichmiiller theory undertaken in the years 1980-1986. Since then many of our colleagues have encouraged us to publish our approach to the subject in a concise format, easily accessible to a broad mathematical audience. However, it was the invitation by the faculty of the ETH Ziirich to deliver the ETH N achdiplom-Vorlesungen on this material which provided the opportunity for the author to develop our research papers into a format suitable for mathematicians with a modest background in differential geometry. We also hoped it would provide the basis for a graduate course stressing the application of fundamental ideas in geometry. For this opportunity the author wishes to thank Eduard Zehnder and Jiirgen Moser, acting director and director of the Forschungsinstitut fiir Mathematik at the ETH, Gisbert Wiistholz, responsible for the Nachdiplom Vorlesungen and the entire ETH faculty for their support and warm hospitality. This new approach to Teichmiiller theory presented here was undertaken for two reasons. First, it was clear that the classical approach, using the theory of extremal quasi-conformal mappings (in this approach we completely avoid the use of quasi-conformal maps) was not easily applicable to the theory of minimal surfaces, a field of interest of the author over many years. Second, many other active mathematicians, who at various times needed some Teichmiiller theory, have found the classical approach inaccessible to them.

Keywords

Minimal surface Riemannian geometry curvature diffeomorphism differential geometry manifold

Authors and affiliations

  • Anthony J. Tromba
    • 1
    • 2
  1. 1.Mathematisches InstitutLudwig-Maximilians-Universität MünchenMünchen 2Germany
  2. 2.Department of MathematicsUniversity of CaliforniaSanta CruzUSA

Bibliographic information