|
A boundary value problem for Hermitian harmonic maps and applications
Author(s):
Jingyi
Chen
Journal:
Proc. Amer. Math. Soc.
124
(1996),
2853-2862.
MSC (1991):
Primary 58E20, 53C55
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We study the existence and uniqueness problems for Hermitian harmonic maps from Hermitian manifolds with boundary to Riemannian manifolds of nonpositive sectional curvature and with convex boundary. The complex analyticity of such maps and the related rigidity problems are also investigated.
References:
- [Boc]
- S. Bochner, Analytic and meromorphic continuation by means of Green's formula, Ann. of Math. 44 (1943), 652--673. MR 5:116f
- [C]
- Jih-Hsin Cheng, Chain-preserving diffeomorphisms and CR equivalence, Proc. Amer. Math. Soc. 103 (1988), 75--80.
- [Co]
- K. Corlette, Archimedian superrigidity and hyperbolic geometry, Ann. of Math. (2) 135 (1992), 165--182. MR 92m:57048
- [CL]
- J.Y. Chen and S.Y. Li, On the holomorphic extension of maps from the boundary of Kähler manfolds, preprint, 1994.
- [GS]
- M. Gromov and R. Schoen, Harmonic maps into singular spaces and p-adic superrigidity for lattices in groups of rank one, Inst. Hautes Études Sci. Publ. Math. 76 (1992), 165--246. MR 94e:58032
- [Ham]
- R. Hamilton, Harmonic maps of manifolds with boundary, Lecture Notes in Math., vol. 471, Springer, New York, 1975. MR 58:2872
- [J1]
- H. Jacobowitz, Chains in CR geometry, J. Differential Geom. 21 (1985), 163--194.MR 87f:32046
- [J2]
- ------, An introduction to CR structures, Math. Surveys Monographs, vol. 32, Amer. Math. Soc., Providence, RI, 1990. MR 93h:32023
- [JY1]
- J. Jost and S.T. Yau, A nonlinear elliptic system for maps from Hermitian to Riemannian manifolds and rigidity theorems in Hermitian geometry, Acta Math. 170 (1993), 221--254. MR 94g:58053
- [JY2]
- ------, The strong rigidity of locally symetric complex manifolds of rank one and finite volume, Math. Ann. 275 (1986), 291--304.
- [JY3]
- ------, On the rigidity of certain discrete groups and algebriac varieties, Math. Ann. 278 (1987), 481--496.
- [M1]
- N. Mok, The holomorphic or antiholomorphic character of harmonic maps into irreducible compact quotients of polydiskc, Math. Ann. 272 (1985), 197--216. MR 86m:22013
- [M2]
- ------, Strong rigidity of irreducible quotients of polydisks of finite volume, Math. Ann. 282 (1988), 555--578.
- [NS]
- S. Nishikawa and K. Shiga, On the holomorphic equivalence of bounded domains in complete Kähler manifolds of nonpositive curvature, J. Math. Soc. Japan 35 (1983), 273--278. MR 84i:32032
- [R]
- R. Remmert, Holomorphie und meromorphe Abbildungen komplexer Räume, Math. Ann. 133 (1957), 328--370. MR 19:1193d
- [S1]
- Y.T. Siu, The complex-analyticity of harmonic maps and the strong rigidity of compact Kähler manifolds, Ann. of Math. (2) 112 (1980), 73--111. MR 81j:53061
- [S2]
- ------, Complex-analyticity of harmonic maps, vanishing and Lefschetz theorems, J. Differential Geom. 17 (1982), 55--138. MR 83j:58039
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
58E20, 53C55
Retrieve articles in all Journals with MSC
(1991):
58E20, 53C55
Additional Information:
Jingyi
Chen
Affiliation:
Department of Mathematics, University of California, Irvine, California 92717
Address at time of publication:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
DOI:
10.1090/S0002-9939-96-03125-5
PII:
S 0002-9939(96)03125-5
Received by editor(s):
July 22, 1994
Additional Notes:
The author was partially supported by NSF grant \#9300422
Communicated by:
Peter Li
Copyright of article:
Copyright
1996,
American Mathematical Society
|
Comments: webmaster@ams.org