An embedding theorem of complete Kähler manifolds of positive bisectional curvature onto affine algebraic varieties
Mok, Ngaiming
Bulletin de la Société Mathématique de France, Tome 112 (1984), p. 197-258 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{BSMF_1984__112__197_0,
     author = {Mok, Ngaiming},
     title = {An embedding theorem of complete K\"ahler manifolds of positive bisectional curvature onto affine algebraic varieties},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     volume = {112},
     year = {1984},
     pages = {197-258},
     doi = {10.24033/bsmf.2005},
     mrnumber = {87a:53103},
     zbl = {0536.53062},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BSMF_1984__112__197_0}
}

Mok, Ngaiming. An embedding theorem of complete Kähler manifolds of positive bisectional curvature onto affine algebraic varieties. Bulletin de la Société Mathématique de France, Tome 112 (1984) pp. 197-258. doi : 10.24033/bsmf.2005. http://gdmltest.u-ga.fr/item/BSMF_1984__112__197_0/

[1] Andreotti (A.) and Vesentini (E.). - Carleman estimates for the Laplace-Beltrami operator on complex manifolds, Publ. Math. Inst. Hautes Études Sci. 25 (1965), 81-130. | Numdam | MR 30 #5333 | Zbl 0138.06604

[2] Bishop (R. L.) and Goldberg (S. I.). - On the second cohomology group of a Kähler manifold of positive curvature, Proc. Amer. Math. Soc. 16 (19765), 119-122. | MR 30 #2441 | Zbl 0125.39403

[3] Bombieri (E.) and Giusti (E.). - Harnack's inequality for elliptic differential equations on minimal surfaces, Inv. Math. 15 (1972), 24-46. | MR 46 #8057 | Zbl 0227.35021

[4] Cheeger (J.) and Ebin (D. G.). - Comparison Theorems in Riemannian Geometry, North-Holland Publishing Co., Amsterdam, 1975. | MR 56 #16538 | Zbl 0309.53035

[5] Cheeger (J.) and Gromoll (D.). - The splitting theorem for manifolds of non-negative Ricci curvature, J. Diff. Geom., 6, (1971), 119-128. | MR 46 #2597 | Zbl 0223.53033

[6] Cheeger (J.) and Gromoll (D.). - On the structure of complete manifolds of non-negative curvature, Ann. of Math. 96 (1972), 413-443. | MR 46 #8121 | Zbl 0246.53049

[7] Cheng (S.-Y.) and Yau (S.-T.). - Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975), 333-354. | MR 52 #6608 | Zbl 0312.53031

[8] Croke (C.). - Some isoperimetric inequalities and consequences, Ann. Scient. Ec. Norm. Sup. 13 (1980). | Numdam | MR 83d:58068 | Zbl 0465.53032

[9] Greene (R. E.) and Wu (H.). - Analysis on non-compact Kähler manifolds, Proc. Symp. Pure Math., Vol. 30, Part II, Amer. Math. Soc. (1977). | Zbl 0383.32005

[10] Greene (R. E.) and Wu (H.). - Function Theory on Manifolds which Possess a Pole, Lecture Notes in Math., Vol. 669, Springer-Verlag, Berlin-Heidelberg-New York, 1979. | MR 81a:53002 | Zbl 0414.53043

[11] Goodman (J. E.). - Affine open subsets of algebraic varieties and ample divisors, Ann. of Math. 89 (1969), 160-183. | MR 39 #4170 | Zbl 0159.50504

[12] Hörmander (L.). - L2-estimates and existence theorems for the ∂-operator, Acta. Math. 113 (1965), 89-152. | Zbl 0158.11002

[13] Lelong (P.). - Fonctions entières (n variables) et fonctions pluri-sousharmoniques d'ordre fini dans Cn, J. Anal. Math. 12 (1964), 365-407. | MR 29 #3668 | Zbl 0126.29602

[14] Lelong (P.). - Sur la structure des courants positifs fermés, Séminaire Pierre Lelong (Analyse), Année 1975/1976, Lectures Notes in Math., Vol. 578, pp. 136-156, Springer-Verlag, Berlin-Heidelberg-New York. | MR 58 #6328 | Zbl 0354.32014

[15] Mok (N.). - Courbure bisectionnelle positive et variétés algébriques affines, Comptes Rendus, Acad. Sc. Paris, Vol. 296, Série A (1983), 473-476. | MR 85a:32015 | Zbl 0579.53043

[16] Mok (N.). - Complete non-compact Kähler manifolds of positive curvature, Complex Analysis of Several Variables, Proc. of Sym. in Pure Math., Vol. 41, Amer. Math. Soc., 1984. | MR 85i:53071 | Zbl 0537.53054

[17] Mok (N.), Siu (Y.-T.) and Yau (S.-T.). - The Poincaré-Lelong equation on complete Kähler manifolds, Comp. Math., Vol. 44, Fasc. 1-3 (1981), 183-218. | Numdam | MR 84g:32011 | Zbl 0531.32007

[18] Moser (J.). - On Harnack's theorem for elliptic differential equations, Comm. Pure and Appl. Math., 14 (1961), 577-591. | MR 28 #2356 | Zbl 0111.09302

[19] Ramanujam (C. P.). - A topological characterization of the affine plane as an algebraic variety, Ann. of Math. 94 (1971), 69-88. | MR 44 #4010 | Zbl 0218.14021

[20] Serre (J.-P.). - Faisceaux algébriques cohérents, Ann. of Math. 61 (1955), 197-278. | MR 16,953c | Zbl 0067.16201

[21] Serre (J.-P.). - Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier 6 (1956), 1-42. | Numdam | MR 18,511a | Zbl 0075.30401

[22] Siu (Y.-T.). - Pseudoconvexity and the problem of Levi, Bull. Amer. Math. Soc. 84 (1978), 481-512. | MR 57 #16648 | Zbl 0423.32008

[23] Siu (Y.-T.). - Analyticity of sets associated to Lelong numbers and the extension of closed positive currents, Invent. Math. 27 (1874), 53-156. | MR 50 #5003 | Zbl 0289.32003

[24] Siu (Y.-T.) and Yau (S.-T.). - Complete Kähler manifolds with non-positive curvature of faster than quadratic decay, Ann. Math. 105 (1977), 225-264. | MR 55 #10719 | Zbl 0358.32006

[25] Skoda (H.). - Application des tachniques L2 à la théorie des idéaux d'une algèbre de fonctions holomorphes avec poids, Ann. Scient. Ec. Norm. Sup. 5 (1972), 548-580. | Numdam | MR 48 #11571 | Zbl 0254.32017

[26] Stampachia (G.). - Equations elliptiques du second ordre à coefficients discontinus, Séminaire de Mathématiques Supérieures 16, 1966. | MR 40 #4603 | Zbl 0151.15501

[27] Thie (P.). - The Lelong number in a point of a complex analytic set, Math. Ann. 172 (1967), 269-312. | MR 35 #5661 | Zbl 0158.32804

[28] Yau (S.-T.). - Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201-228. | MR 55 #4042 | Zbl 0291.31002

[29] Blanc (C.) and Fiala (F.). - Le type d'une surface et sa courbure totale, Comment. Math. Helv. 14 (1941-1942), 230-233. | MR 4,53d | Zbl 0026.01501

[30] Gromoll (D.) and Meyer (W.). - On complete open manifolds of non-negative curvature, Ann. of Math. 90 (1969), 75-90. | MR 40 #854 | Zbl 0191.19904

[31] Poor (W.). - Some results on nonnegatively curved manifolds, J. Diff. Geom. 9 (1974), 583-600. | MR 51 #11351 | Zbl 0292.53037

[32] Wu (H.). - An elemetary method in the study of nonnegative curvature, Acta Math. 142 (1979), 57-78. | MR 80c:53054 | Zbl 0403.53022