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Harmonic Maps between Riemannian Polyhedra: 142
Author(s): Preface by M. Gromov J. Eells, B. Fuglede (Author)
- Publisher: Cambridge University Press
- Publication Date: 2 Aug. 2001
- Edition: 1st
- Language: English
- Print length: 312 pages
- ISBN-10: 0521773113
- ISBN-13: 9780521773119
Book Description
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.
Editorial Reviews
Review
‘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
Book Description
A research level book on harmonic maps between singular spaces, by renowned authors, first published in 2001.
