Hölder continuity of harmonic maps from Riemannian polyhedra to spaces of upper bounded curvature |
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Authors: | Bent Fuglede |
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Institution: | Department of Mathematics, Universitetsparken 5, DK-2100 Copenhagen ?, Denmark; e-mail: fuglede@math.ku.dk; homepage: www.math.ku.dk/ fuglede., DK
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Abstract: | This is an addendum to the recent Cambridge Tract “Harmonic maps between Riemannian polyhedra”, by J. Eells and the present
author. H?lder continuity of locally energy minimizing maps from an admissible Riemannian polyhedron X to a complete geodesic space Y is established here in two cases: (1) Y is simply connected and has curvature (in the sense of A.D. Alexandrov), or (2) Y is locally compact and has curvature , say, and is contained in a convex ball in Y satisfying bi-point uniqueness and of radius (best possible). With Y a Riemannian polyhedron, and in case (2), this was established in the book mentioned above, though with H?lder continuity taken in a weaker, pointwise
sense. For X a Riemannian manifold the stated results are due to N.J. Korevaar and R.M. Schoen, resp. T. Serbinowski.
Received: 10 October 2001 / Accepted: 20 November 2001 / Published online: 6 August 2002 |
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Keywords: | Mathematics Subject Classification (1991): 58E20 49N60 53C22 |
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