Springer Monographs in Mathematics

Constant Mean Curvature Surfaces with Boundary

Authors: López, Rafael

  • Includes set of interesting open problems
  • First comprehensive publication on "compact surfaces with boundary"
  • Gives a state-of-the-art review of the theory
see more benefits

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-642-39626-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-642-39625-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-3-662-51256-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this book

The study of surfaces with constant mean curvature (CMC) is one of the main topics in classical differential geometry. Moreover, CMC surfaces are important mathematical models for the physics of interfaces in the absence of gravity, where they separate two different media or for capillary phenomena. Further, as most techniques used in the theory of CMC surfaces not only involve geometric methods but also PDE and complex analysis, the theory is also of great interest for many other mathematical fields.

While minimal surfaces and CMC surfaces in general have already been treated in the literature, the present work is the first to present a comprehensive study of “compact surfaces with boundaries,” narrowing its focus to a geometric view. Basic issues include the discussion whether the symmetries of the curve inherit to the surface; the possible values of the mean curvature, area and volume; stability; the circular boundary case and the existence of the Plateau problem in the non-parametric case. The exposition provides an outlook on recent research but also a set of techniques that allows the results to be expanded to other ambient spaces. Throughout the text, numerous illustrations clarify the results and their proofs.

The book is intended for graduate students and researchers in the field of differential geometry and especially theory of surfaces, including geometric analysis and geometric PDEs. It guides readers up to the state-of-the-art of the theory and introduces them to interesting open problems.

About the authors

R. López, Professor at the University of Granada’s Department of Geometry and Topology has published more than 70 articles, many of them in journals with high Impact Factors (Duke Math. J., J. Diff. Eq. Calculus of Var., Comm. Math. Phys. SIAM J. Math. Anal.) and has served as a visiting professor at Paris VII, Idaho St. Univ., Sao Paulo, Toledo, Iasi and KIAS. His main research area is ‘surfaces with prescribed mean curvature,’ including elliptic equations and general relativity.

Table of contents (12 chapters)

  • A Brief Historical Introduction and Motivations

    López, Rafael

    Pages 1-12

  • Surfaces with Constant Mean Curvature

    López, Rafael

    Pages 13-36

  • The Comparison and Tangency Principles

    López, Rafael

    Pages 37-54

  • Constant Mean Curvature Embedded Surfaces

    López, Rafael

    Pages 55-79

  • The Flux Formula for Constant Mean Curvature Surfaces

    López, Rafael

    Pages 81-101

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-642-39626-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-642-39625-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-3-662-51256-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Constant Mean Curvature Surfaces with Boundary
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-39626-7
DOI
10.1007/978-3-642-39626-7
Hardcover ISBN
978-3-642-39625-0
Softcover ISBN
978-3-662-51256-2
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XIV, 292
Number of Illustrations and Tables
64 b/w illustrations
Topics