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Harmonic Maps between Riemannian Polyhedra : Cambridge Tracts in Mathematics (Hardcover) - James Eelles

Harmonic Maps between Riemannian Polyhedra

Cambridge Tracts in Mathematics (Hardcover)

By: James Eelles, Bent Fuglede, M. Gromov (Preface by)

Hardcover

Published: 5th September 2011
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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.

'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

GromovÆs preface
Preface
Introduction
Domains, Targets, Examples
Harmonic spaces, Dirichlet spaces and geodesic spaces
Examples of domains and targets
Riemannian polyhedra
Potential Theory on Polyhedra
The Sobolev space W1,2(X). Weakly harmonic functions
Potential theory on Riemannian polyhedra
Examples of Riemannian polyhedra and related spaces
Maps between Polyhedra
Energy of maps
Hölder continuity of energy minimizers
Existence of energy minimizers
Harmonic maps - totally geodesic maps
Harmonic morphisms
Energy according to Korevaar-Schoen
Minimizers with small energy decay
Bibliography
Special symbols
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521773119
ISBN-10: 0521773113
Series: Cambridge Tracts in Mathematics (Hardcover)
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 312
Published: 5th September 2011
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 2.06
Weight (kg): 0.63