On the Dirichlet problem for harmonic maps with prescribed singularities
Gilbert Weinstein
Source: Duke Math. J. Volume 77, Number 1
(1995), 135-165.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077286149
Mathematical Reviews number (MathSciNet): MR1317630
Zentralblatt MATH identifier: 0829.53041
Digital Object Identifier: doi:10.1215/S0012-7094-95-07706-0
References
[1] R. Bach and H. Weyl, Neue Lösungen der Einsteinschen Gravitationsgleichungen, Math. Z. 13 (1921), 132–145.
[2] M. T. Anderson, Complete minimal hypersurfaces in hyperbolic $n$-manifolds, Comment. Math. Helvetici 58 (1983), no. 2, 264–290.
Mathematical Reviews (MathSciNet): MR85e:53076
Zentralblatt MATH: 0549.53058
Digital Object Identifier: doi:10.1007/BF02564636
[3] P. Eberlein and B. O'Neill, Visibility manifolds, Pacific J. Math. 46 (1973), 45–109.
Mathematical Reviews (MathSciNet): MR49:1421
Zentralblatt MATH: 0264.53026
Project Euclid: euclid.pjm/1102946601
[4] R. Hamilton, Harmonic Maps of Manifolds with Boundary, Lecture Notes in Math., vol. 471, Springer-Verlag, Berlin, 1975.
Mathematical Reviews (MathSciNet): MR58:2872
Zentralblatt MATH: 0308.35003
[5] E. Heintze and H. C. Im Hof, Geometry of horospheres, J. Differential Geom. 12 (1977), no. 4, 481–491.
Mathematical Reviews (MathSciNet): MR80a:53051
Zentralblatt MATH: 0434.53038
Project Euclid: euclid.jdg/1214434219
[6] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Pure Appl. Math., vol. 80, Academic Press, Boston, 1978.
Mathematical Reviews (MathSciNet): MR80k:53081
Zentralblatt MATH: 0451.53038
[7] P. Li and L.-F. Tam, The heat equation and harmonic maps of complete manifolds, Invent. Math. 105 (1991), no. 1, 1–46.
Mathematical Reviews (MathSciNet): MR93e:58039
Zentralblatt MATH: 0748.58006
Digital Object Identifier: doi:10.1007/BF01232256
[8] P. Li and L.-F. Tam, Uniqueness and regularity of proper harmonic maps, Ann. Math. (2) 137 (1993), no. 1, 167–201.
Mathematical Reviews (MathSciNet): MR93m:58027
Zentralblatt MATH: 0776.58010
Digital Object Identifier: doi:10.2307/2946622
JSTOR: links.jstor.org
[9] Y. Li and G. Tian, Regularity of harmonic maps with prescribed singularities, Comm. Math. Phys. 149 (1992), no. 1, 1–30.
Mathematical Reviews (MathSciNet): MR94f:58036
Zentralblatt MATH: 0785.53047
Digital Object Identifier: doi:10.1007/BF02096622
Project Euclid: euclid.cmp/1104251137
[10] Y. Li and G. Tian, Harmonic maps with prescribed singularities, Differential Geometry: Partial Differential Equations on Manifolds (Los Angeles, CA, 1990), Proc. Symp. Pure Math., Part 1, vol. 54, Amer. Math. Soc., Providence, 1993, pp. 317–326.
Mathematical Reviews (MathSciNet): MR94d:58047
Zentralblatt MATH: 0826.35035
[11] P. O. Mazur, Proof of uniqueness of the Kerr-Newman black hole solution, J. Phys. A 15 (1982), no. 10, 3173–3180.
Mathematical Reviews (MathSciNet): MR84j:83013
Zentralblatt MATH: 1141.83304
Digital Object Identifier: doi:10.1088/0305-4470/15/10/021
[12] G. D. Mostow, Strong Rigidity of Locally Symmetric Spaces, Ann. Math. Stud., vol. 78, Princeton University Press, Princeton, 1973.
Mathematical Reviews (MathSciNet): MR52:5874
Zentralblatt MATH: 0265.53039
[13] R. Schoen and K. Uhlenbeck, A regularity theory for harmonic maps, J. Differential Geom. 17 (1982), no. 2, 307–335.
Mathematical Reviews (MathSciNet): MR84b:58037a
Zentralblatt MATH: 0521.58021
Project Euclid: euclid.jdg/1214436923
[14] R. Schoen and K. Uhlenbeck, Boundary regularity and the Dirichlet problem for harmonic maps, J. Differential Geom. 18 (1983), no. 2, 253–268.
Mathematical Reviews (MathSciNet): MR85b:58037
Zentralblatt MATH: 0547.58020
Project Euclid: euclid.jdg/1214437663
[15] R. Schoen and S. T. Yau, Compact group actions and the topology of manifolds with non-positive curvature, Topology 18 (1979), no. 4, 361–380.
Mathematical Reviews (MathSciNet): MR81a:53044
Zentralblatt MATH: 0424.58012
Digital Object Identifier: doi:10.1016/0040-9383(79)90026-0
[16] Y. Shen, A Liouville theorem for harmonic maps, Amer. J. Math. to appear.
Mathematical Reviews (MathSciNet): MR1333944
Zentralblatt MATH: 0839.53027
Digital Object Identifier: doi:10.2307/2375088
JSTOR: links.jstor.org
[17] L. Simon, Lectures on Geometric Measure Theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, vol. 3, Australian National University, Canberra, 1983.
Mathematical Reviews (MathSciNet): MR87a:49001
Zentralblatt MATH: 0546.49019
[18] G. Weinstein, On rotating black holes in equilibrium in general relativity, Comm. Pure Appl. Math. 43 (1990), no. 7, 903–948.
Mathematical Reviews (MathSciNet): MR91h:83063
Zentralblatt MATH: 0709.53063
Digital Object Identifier: doi:10.1002/cpa.3160430705
[19] G. Weinstein, The stationary axisymmetric two-body problem in general relativity, Comm. Pure Appl. Math. 45 (1992), no. 9, 1183–1203.
Mathematical Reviews (MathSciNet): MR93k:83010
Zentralblatt MATH: 0782.53088
Digital Object Identifier: doi:10.1002/cpa.3160450907
Duke Mathematical Journal
