References
[AGV] Arnold, V.I., Gusein-Zade, S.M., Varchenko, A.N.: Singularities of differentiable maps, vol. II. Monogr. Math.,83, Boston Basel Stuttgart, Birkhaüser 1988
[An] Anderson, M.: Ricci curvature bounds and Einstein metrics on compact manifolds. Preprint
[Au] Aubin, T.: Réduction du cas positif de l'équation de Monge-Ampère sur les variétés Kählerinnes compactes à la démonstration d'un intégalité. J. Funct. Anal.57, 143–153 (1984)
[Bai] Baily, W.: On the imbedding of V-manifolds in projective space. Am. J. Math.79, 403–430 (1957)
[Ban] Bando, S.: The K-energy map, almost Einstein-Kähler metrics mnd an inequality of the Miyaoka-Yau type. Tohoku Math. J.39, 231–235 (1987)
[Bi] Bishop, R.L., Crittenden, R.J.: Geometry of Manifolds, Pure and Applied Math., Vol. XV. New York-London: Academic Press 1964
[BM] Bando, S., Mabuchi, T.: Uniqueness of Einstein Kähler metrics modulo connected group actions. In: Oda T. (ed.) Alg. Geom., Sendai, Adv. Stud. Pure Math.10, Kinokunia, Tokyo and North Holland, Amsterdam, New York, Oxford, 1985
[BPV] Barth, W., Peters, C., Van de Ven, A.: Compact complex surfaces. Berlin-Heidelberg-New York: Springer 1984
[CE] Cheeger, J., Ebin, D.G.: Comparison theorems in Riemannian geometry. North-Holland Publishing Company, Amsterdam, 1975
[CGT] Cheeger, J., Gromov, M., Taylor, M.: Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds. J. Differ. Geom.17, 15–54 (1982)
[Cr] Croke, C.: Some isoperimetric inequalities and eigenvalue estimates. Ann. Sci. Ec. Norm. Super, Ser.13, 419–435 (1980)
[De] Demazure, M.: Surfaces de Del Pezzo. (Lecture Notes in Math., vol. 777, pp. 21–69). Berlin-Heidelberg-New York: Springer 1980
[Fu] Futaki, S.: An obstruction to the existence of Einstein-Kähler metrics. Invent. Math.73, 437–443 (1983)
[GH] Griffith, P., Harris, J.: Principles of Algebraic Geometry. New York: Wiley, 1978
[GLP] Gromov, M., Lafontaine, J., Pansu, P.: Structure metrique pour les varietes Riamanniennes. Nathen: Cedic/Fernand 1981
[GT] Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Berlin-Heidelberg-New York: Springer 1977
[GW] Greene, R., Wu, H.: Lipschitz convergence of Riemannian manifolds. Pac. J. Math.131, 119–141 (1988)
[Ho] Hömander, L.: An introduction to complex analysis in several variables. Princeton: Van Nostrand 1973
[Jo] Jost, J.: Harmonic mappings between Riemannian manifolds. Proceedings of the center for mathematical analysis. Australian National Univ., Vol. 4, 1983
[KM] Kodaira, K., Morrow, J.: Complex manifolds. Holt-Rinehart and Winston, Inc: New York 1971
[KT] Kazdan, J., DeTurke, D.: Some regularity theorems in Riemannian geometry. Ann. Sci. Ec. Norm. Super, IV. Ser.14, 249–260 (1981)
[La] Laufer, H.: Normal two-dimensional singularities. Ann. Math. Stud.71, Princeton University Press 1971
[Le] Lelong, P.: Fonctions plurisousharmoniques et forms différentielles positives. New York: Gondon and Breach et Paris, Dunod 1969
[Li] Li, P.: On the Sobolev constant and the p-spectrum of a compact Riemannian manifols. Ann. Sci. Ec. Norm. Super, IV. Ser.13, 451–469 (1980)
[Ma] Matsushima, Y.: Sur la structure du group d'homeomorphismes analytiques d'une certaine varietie Kaehlerinne. Nagoya Math. J.11, 145–150 (1957)
[Na] Nakajima, H.: Hausdorff convergence of Einstein 4-manifolds. J. Fac. Sci. Univ. Tokyo35, 411–424 (1988)
[Si] Siu, Y.T.: The existence of Kähler-Einstein metrics on manifolds with positive anticanonical line bundle and a suitable finite symmetry group. Ann. Math.127, 585–627 (1988)
[T1] Tian, G.: On Kähler-Einstein metrics on certain Kähler manifolds withC 1(M)>0. Invent. Math.89, 225–246 (1987)
[T2] Tian, G.: A Harnack inequality for some complex Monge-Ampére equations. (To appear) J. Differ. Geom.
[TY] Tian, G., Yau, S.T.: Kähler-Einstein metrics on complex surfaces withC 1(M) positive. Commun. Math. Phys.112, 175–203 (1987)
[Uh1] Uhlenbeck, K.: Removable singularities in Yang-Mills field. Commun. Math. Phys.83, 11–29 (1982)
[Uh2] Uhlenbeck, K.: Connections withL p bounds on Curvature. Commun. Math. Phys.83, 31–42 (1982)
[Y1] Yau, S.T.: On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampére equation,I *. Commun. Pure Appl. Math.31, 339–411 (1978)
[Y2] Yau, S.T.: On Calabi's conjecture and some new results in algebraic geometry. Proc. Natl. Acad. Sci. USA74, 1798–1799 (1977)
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Oblatum 23-III-1989
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Tian, G. On Calabi's conjecture for complex surfaces with positive first Chern class. Invent Math 101, 101–172 (1990). https://doi.org/10.1007/BF01231499
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DOI: https://doi.org/10.1007/BF01231499