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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Deforming a map into a harmonic map


Author: Deane Yang
Journal: Trans. Amer. Math. Soc. 352 (2000), 1021-1038
MSC (1991): Primary 58G30
DOI: https://doi.org/10.1090/S0002-9947-99-02402-2
Published electronically: March 8, 1999
MathSciNet review: 1624222
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Abstract: This paper presents some existence and uniqueness theorems for harmonic maps between complete noncompact Riemannian manifolds. In particular, we obtain as a corollary a recent result of Hardt-Wolf on the existence of harmonic quasi-isometries of the hyperbolic plane.


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Additional Information

Deane Yang
Affiliation: Department of Mathematics, Polytechnic University, Six Metrotech Center, Brooklyn, New York 11201
Email: yang@math.poly.edu

DOI: https://doi.org/10.1090/S0002-9947-99-02402-2
Received by editor(s): July 10, 1997
Received by editor(s) in revised form: December 20, 1997
Published electronically: March 8, 1999
Additional Notes: I was partially supported by National Science Foundation grant DMS-9200576. Some of the work in this paper was done at l’Institut des Hautes Etudes Scientifiques. I would like thank the staff and the director, Jean–Pierre Bourguignon, for their support and hospitality. I would also like to thank Stephen Semmes, Curt McMullen, and Michael Wolf for helpful discussions. I am grateful to Peter Li and the referee for their comments on an earlier version of this paper and references to related results.
Article copyright: © Copyright 1999 American Mathematical Society