Harmonic Maps Between Riemannian Polyhedra

Front Cover
Cambridge University Press, Jul 30, 2001 - Mathematics - 296 pages
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.
 

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Contents

Harmonic spaces Dirichlet spaces and geodesic spaces
15
Examples of domains and targets
30
Riemannian polyhedra
41
The Sobolev space W12X
63
Weakly harmonic and weakly subsuperharmonic functions
72
Harnack inequality and Holder continuity for weakly
79
Potential theory on Riemannian polyhedra
99
Examples of Riemannian polyhedra and related spaces
130
Holder continuity of energy minimizers
178
Existence of energy minimizers
198
Harmonic maps Totally geodesic maps
217
Harmonic i nor phis iris
247
Energy according to KorevaarSchoen
259
Bibliography
277
Special symbols
291
Copyright

Energy of maps
151

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