A boundary value problem for Hermitian harmonic maps and applications
HTML articles powered by AMS MathViewer
- by Jingyi Chen
- Proc. Amer. Math. Soc. 124 (1996), 2853-2862
- DOI: https://doi.org/10.1090/S0002-9939-96-03125-5
- PDF | Request permission
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
- Albert Eagle, Series for all the roots of a trinomial equation, Amer. Math. Monthly 46 (1939), 422–425. MR 5, DOI 10.2307/2303036
- Jih-Hsin Cheng, Chain-preserving diffeomorphisms and CR equivalence, Proc. Amer. Math. Soc. 103 (1988), 75–80.
- Kevin Corlette, Archimedean superrigidity and hyperbolic geometry, Ann. of Math. (2) 135 (1992), no. 1, 165–182. MR 1147961, DOI 10.2307/2946567
- J.Y. Chen and S.Y. Li, On the holomorphic extension of maps from the boundary of Kähler manfolds, preprint, 1994.
- Mikhail Gromov and Richard 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 1215595, DOI 10.1007/BF02699433
- Richard S. Hamilton, Harmonic maps of manifolds with boundary, Lecture Notes in Mathematics, Vol. 471, Springer-Verlag, Berlin-New York, 1975. MR 482822, DOI 10.1007/BFb0087227
- Howard Jacobowitz, Chains in CR geometry, J. Differential Geom. 21 (1985), no. 2, 163–194. MR 816668
- Howard Jacobowitz, An introduction to CR structures, Mathematical Surveys and Monographs, vol. 32, American Mathematical Society, Providence, RI, 1990. MR 1067341, DOI 10.1090/surv/032
- Jürgen Jost and Shing-Tung Yau, A nonlinear elliptic system for maps from Hermitian to Riemannian manifolds and rigidity theorems in Hermitian geometry, Acta Math. 170 (1993), no. 2, 221–254. MR 1226528, DOI 10.1007/BF02392786
- —, The strong rigidity of locally symetric complex manifolds of rank one and finite volume, Math. Ann. 275 (1986), 291–304.
- —, On the rigidity of certain discrete groups and algebriac varieties, Math. Ann. 278 (1987), 481–496.
- Ngaiming Mok, The holomorphic or antiholomorphic character of harmonic maps into irreducible compact quotients of polydiscs, Math. Ann. 272 (1985), no. 2, 197–216. MR 796247, DOI 10.1007/BF01450565
- —, Strong rigidity of irreducible quotients of polydisks of finite volume, Math. Ann. 282 (1988), 555–578.
- Seiki Nishikawa and Kiyoshi Shiga, On the holomorphic equivalence of bounded domains in complete Kähler manifolds of nonpositive curvature, J. Math. Soc. Japan 35 (1983), no. 2, 273–278. MR 692326, DOI 10.2969/jmsj/03520273
- Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
- Yum Tong Siu, The complex-analyticity of harmonic maps and the strong rigidity of compact Kähler manifolds, Ann. of Math. (2) 112 (1980), no. 1, 73–111. MR 584075, DOI 10.2307/1971321
- Yum Tong Siu, Complex-analyticity of harmonic maps, vanishing and Lefschetz theorems, J. Differential Geometry 17 (1982), no. 1, 55–138. MR 658472
Bibliographic 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
- Received by editor(s): July 22, 1994
- Additional Notes: The author was partially supported by NSF grant #9300422
- Communicated by: Peter Li
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 2853-2862
- MSC (1991): Primary 58E20, 53C55
- DOI: https://doi.org/10.1090/S0002-9939-96-03125-5
- MathSciNet review: 1301014