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Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli

  • Gabor Toth

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Gabor Toth
    Pages 1-93
  3. Gabor Toth
    Pages 95-170
  4. Gabor Toth
    Pages 171-240
  5. Back Matter
    Pages 283-319

About this book

Introduction

"Spherical soap bubbles", isometric minimal immersions of round spheres into round spheres, or spherical immersions for short, belong to a fast growing and fascinating area between algebra and geometry. This theory has rich inteconnections with a variety of mathematical disciplines such as invariant theory, convex geometry, harmonic maps, and orthogonal multiplications. In this book, the author traces the development of the study of spherical minimal immersions over the past 30 plus years, including Takahashi's 1966 proof regarding the existence of isometric minimal immersions, DoCarmo and Wallach's study of the uniqueness of the standard minimal immersion in the seventies, and the mor recent study of the variety of spherical minimal immersions which have been obtained by the "equivariant construction" as SU(2)-orbits, first used by Mashimo in 1984 and then later by DeTurck and Ziller in 1992. In trying to make this monograph accessible not just to research mathematicians but mathematics graduate students as well, the author included sizeable pieces of material from upper level undergraduate courses, additional graduate level topics such as Felix Kleins classic treatise of the icosahedron, and a valuable selection of exercises at the end of each chapter.

Keywords

Finite Möbius Groups Riemannian geometry minimum spherical minimal immersions spherical soap bubles

Authors and affiliations

  • Gabor Toth
    • 1
  1. 1.Department of Mathematical SciencesRutgers University, CamdenCamdenUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-0061-8
  • Copyright Information Springer-Verlag New York, Inc. 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6546-7
  • Online ISBN 978-1-4613-0061-8
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site
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