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Harmonic Maps between Riemannian Polyhedra

Harmonic Maps between Riemannian Polyhedra

$131.00 (C)

Part of Cambridge Tracts in Mathematics

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

$ 131.00 (C)

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About the Authors
  • This research-level monograph on harmonic maps between singular spaces sets out much new material on the theory, bringing all the research together for the first time in one place. Riemannian polyhedra are a class of such spaces that are especially suitable to serve as the domain of definition for harmonic maps. Their properties are considered in detail, with many examples being given, and potential theory on Riemmanian polyhedra is also considered. The work will serve as a concise source and reference for all researchers working in this field or a similar one.

    • 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

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    Product details

    • Date Published: July 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
    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
    Special symbols

  • Authors

    J. Eells, University of Cambridge

    B. Fuglede, University of Copenhagen

    Preface by

    M. Gromov

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