Harmonic Maps between Riemannian Polyhedra

James Eells, Bent Fuglede

296 pages, parution le 01/05/2001

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Résumé

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 30 years, and has significant applications throughout mathematics. This 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 authors set out much new material on harmonic maps between singular spaces for the first time in book form. The work will hence serve as a concise source for all researchers working in related fields.

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
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.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	James Eells, Bent Fuglede
Parution	01/05/2001
Nb. de pages	296
Format	15,5 x 23,5
Couverture	Relié
Poids	550g
Intérieur	Noir et Blanc
EAN13	9780521773119
ISBN13	978-0-521-77311-9