Universitext

Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli

Authors: Toth, Gabor

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eBook 63,06 €
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  • ISBN 978-1-4613-0061-8
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Hardcover 114,39 €
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  • ISBN 978-0-387-95323-6
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Softcover 77,99 €
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  • ISBN 978-1-4612-6546-7
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About this book

"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.

Reviews

From the reviews of the first edition:

"This monograph is devoted to minimal immersions between round spheres. … Indeed, the author’s exposition is largely self-contained – and leisurely. Exercises are abundant, forming an integral part of the presentation. … This monograph has been written with great care. It would be appropriate for an undergraduate or graduate seminar." (J. Ells, Mathematical Reviews, Issue 2002 i)

"In this book, the author traces the development of the study of spherical minimal immersions over the past 30-plus years … . In trying to make this monograph accessible not just to research mathematicians but to mathematics graduate students as well, the author included sizeable pieces of material from upper-level undergraduate courses, additional graduate level topics such as Felix Klein’s classical treatise of the icosahedron, and a valuable selection of exercises." (L’Enseignement Mathematique, Vol. 48 (1-2), 2002)

"This very interesting monograph for researchers and graduate students as well, gives a wide picture of the theory of spherical soap bubbles, which studies isometric minimal immersions of round spheres … . Each chapter ends with some additional topics and some challenging problems. A useful appendix with some basic notions is given at the end of the book." (Cornelia-Livia Bejan, Zentralblatt MATH, Vol. 1074, 2005)


Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook 63,06 €
price for Spain (gross)
  • ISBN 978-1-4613-0061-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 114,39 €
price for Spain (gross)
  • ISBN 978-0-387-95323-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 77,99 €
price for Spain (gross)
  • ISBN 978-1-4612-6546-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli
Authors
Series Title
Universitext
Copyright
2002
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4613-0061-8
DOI
10.1007/978-1-4613-0061-8
Hardcover ISBN
978-0-387-95323-6
Softcover ISBN
978-1-4612-6546-7
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XVI, 319
Topics