Skip to content
Register Sign in Wishlist
Harmonic Maps between Riemannian Polyhedra

Harmonic Maps between Riemannian Polyhedra

$120.00

Part of Cambridge Tracts in Mathematics

  • Date Published: August 2001
  • availability: Available
  • format: Hardback
  • isbn: 9780521773119

$ 120.00
Hardback

Add to cart Add to wishlist

Looking for an inspection copy?

This title is not currently available for inspection. However, if you are interested in the title for your course we can consider offering an inspection copy. To register your interest please contact asiamktg@cambridge.org providing details of the course you are teaching.

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • Harmonic maps between smooth Riemannian manifolds play a ubiquitous role in differential geometry. Examples include geodesics viewed as maps, minimal surfaces, holomorphic maps and Abelian integrals viewed as maps to a circle. The theory of such maps has been extensively developed over the last 40 years, and has significant applications throughout mathematics. This 2001 book extends that theory in full detail to harmonic maps between broad classes of singular Riemannian polyhedra, with many examples being given. The analytical foundation is based on existence and regularity results which use the potential theory of Riemannian polyhedral domains viewed as Brelot harmonic spaces and geodesic space targets in the sense of Alexandrov and Busemann. The work sets out much material on harmonic maps between singular spaces and will hence serve as a concise source for all researchers working in related fields.

    • Written by leading researchers
    • Presents new material which has never before been brought together in book form
    • Unique treatment - there are no directly comparable books on the subject
    Read more

    Reviews & endorsements

    'This book can be highly recommended, both to specialists in the field, who will find a direct interest, and to geometers and analysts, who will find a source containing a large amount of material, with precise references. The organization of the chapters is excellent.' Luc Lemaire, Bulletin of the London Mathematical Society

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: August 2001
    • format: Hardback
    • isbn: 9780521773119
    • length: 312 pages
    • dimensions: 229 x 152 x 21 mm
    • weight: 0.63kg
    • availability: Available
  • Table of Contents

    Gromov's preface
    Preface
    1. Introduction
    Part I. Domains, Targets, Examples:
    2. Harmonic spaces, Dirichlet spaces and geodesic spaces
    3. Examples of domains and targets
    4. Riemannian polyhedra
    Part II. Potential Theory on Polyhedra:
    5. The Sobolev space W1,2(X). Weakly harmonic functions
    6. Harnack inequality and Hölder continuity for weakly harmonic functions
    7. Potential theory on Riemannian polyhedra
    8. Examples of Riemannian polyhedra and related spaces
    Part III. Maps between Polyhedra:
    9. Energy of maps
    10. Hölder continuity of energy minimizers
    11. Existence of energy minimizers
    12. Harmonic maps - totally geodesic maps
    13. Harmonic morphisms
    14. Appendix A. Energy according to Korevaar-Schoen
    15. Appendix B. Minimizers with small energy decay
    Bibliography
    Special symbols
    Index.

  • Authors

    J. Eells, University of Cambridge

    B. Fuglede, University of Copenhagen

    Preface by

    M. Gromov

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×