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Zhang, Xi. Hermitian Yang–Mills–Higgs Metrics on Complete Kähler Manifolds. Canadian journal of mathematics, Tome 57 (2005) no. 4, pp. 871-896. doi: 10.4153/CJM-2005-034-3
@article{10_4153_CJM_2005_034_3,
author = {Zhang, Xi},
title = {Hermitian {Yang{\textendash}Mills{\textendash}Higgs} {Metrics} on {Complete} {K\"ahler} {Manifolds}},
journal = {Canadian journal of mathematics},
pages = {871--896},
year = {2005},
volume = {57},
number = {4},
doi = {10.4153/CJM-2005-034-3},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2005-034-3/}
}
[1] [1] Bradlow, S. B., Vortices in holomorphic line bundles over closed Kähler manifolds. Commun. Math. Phys. 135(1990), 1–17. Google Scholar
[2] [2] Bradlow, S. B., Special metrics and stability for holomorphic bundles with global sections. J. Differential Geom. 33(1991), 169–213. Google Scholar
[3] [3] Cheng, S. Y. and Li, P., Heat kernel estimates and lower bound of eigenvalues. Comment.Math. Helv. 56(1981), 327–338. Google Scholar
[4] [4] Donaldson, S. K., Anti-self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles. Proc. LondonMath. Soc. (3) 50(1985), 1–26. Google Scholar
[5] [5] Donaldson, S. K., Boundary value problems for Yang-Mills fields. J. Geom. Phys. 8(1992), 89–122. Google Scholar
[6] [6] Ding, W. Y. and Y.Wang, Harmonic maps of complete noncompact Riemannian manifolds. Internat. J. Math. 2(1991), 617–633. Google Scholar
[7] [7] Grigor’yan, A., Gaussian upper bounds for the heat kernel on arbitrary manifolds. J. Differential Geom. 45(1997), 33–52. Google Scholar
[8] [8] Gilbarg, D. and Trudinger, N. S., Elliptic partial differential equations of second order. Second edition. Grundlehren der MathematischenWissenschaften 224, Springer-Verlag, Berlin, 1983. Google Scholar
[9] [9] Hamilton, R. S., Harmonic maps of manifolds with boundary. Lecture Notes in Mathematics 471, Springer-Verlag, Berlin, 1975. Google Scholar
[10] [10] Hitchin, N. J., The self-duality equations on a Riemann surface. Proc. LondonMath. Soc. (3) 55(1987), 59–126. Google Scholar
[11] [11] Hong, M. C., Heat flow for the Yang-Mills-Higgs field and the Hermitian Yang-Mills-Higgs metric. Ann. Global Anal. Geom. 20(2001), 23–46. Google Scholar
[12] [12] Li, P. and Tam, L. F., The heat equation and harmonic maps of complete manifolds. Invent.Math. 105(1991), 1–46. Google Scholar
[13] [13] Li, J. Y., The heat flows and harmonic maps of complete noncompact Riemannian manifolds. Math. Z. 212(1993), 161–173. Google Scholar
[14] [14] Moser, J., On Harnack's theorem for elliptic differential equations. Commun. Pure Appl. Math. 14(1961), 577–591. Google Scholar
[15] [15] Nash, J., Continuity of solutions of parabolic and elliptic equations. Amer. J.Math. 80(1958), 931–954. Google Scholar
[16] [16] Ni, L., The Poisson equation and Hermitian-Einstein metrics on holomorphic vector bundles over complete noncompact Kähler manifolds. Indiana. Univ.Math. J. 51(2002), 679–704. Google Scholar
[17] [17] Ni, L. and Ren, H., Hermitian-Einstein metrics on vector bundles on complete Kähler manifolds. Trans. Amer.Math. Soc. 353(2001), 441–456. Google Scholar
[18] [18] Narasimhan, M. S. and Seshadri, C. S., Stable and unitary vector bundles on a compact Riemann surface. Ann. of Math. 82(1965), 540–567. Google Scholar
[19] [19] Saloff-Coste, L., Uniformly elliptic operators on Riemannian manifolds. J. Diff. Geom. 36(1992), 417–450. Google Scholar
[20] [20] Simpson, C. T., Constructing variations of Hodge structures using Yang-Mills theory and applications to uniformization. J. Amer. Math. Soc. 1(1988), 867–918. Google Scholar
[21] [21] Siu, Y. T., Lectures on Hermitian-Einstein metrics for stable bundles and Kahler-Einstein metrics. DMV Seminar 8, Birkhauser Verlag, Basel, 1987. Google Scholar
[22] [22] Uhlenbeck, K. K. and Yau, S.-T., On the existence of Hermitian-Yang-Mills connection in stable vector bundles. Comm. Pure Appl. Math. 39S(1986), S257–S293. Google Scholar
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