@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}, pages = {197--258}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {112}, year = {1984}, doi = {10.24033/bsmf.2005}, mrnumber = {87a:53103}, zbl = {0536.53062}, language = {en}, url = {https://www.numdam.org/articles/10.24033/bsmf.2005/} }
TY - JOUR AU - Mok, Ngaiming TI - An embedding theorem of complete Kähler manifolds of positive bisectional curvature onto affine algebraic varieties JO - Bulletin de la Société Mathématique de France PY - 1984 SP - 197 EP - 258 VL - 112 PB - Société mathématique de France UR - https://www.numdam.org/articles/10.24033/bsmf.2005/ DO - 10.24033/bsmf.2005 LA - en ID - BSMF_1984__112__197_0 ER -
%0 Journal Article %A Mok, Ngaiming %T An embedding theorem of complete Kähler manifolds of positive bisectional curvature onto affine algebraic varieties %J Bulletin de la Société Mathématique de France %D 1984 %P 197-258 %V 112 %I Société mathématique de France %U https://www.numdam.org/articles/10.24033/bsmf.2005/ %R 10.24033/bsmf.2005 %G en %F 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. https://www.numdam.org/articles/10.24033/bsmf.2005/
[1] Carleman estimates for the Laplace-Beltrami operator on complex manifolds, Publ. Math. Inst. Hautes Études Sci. 25 (1965), 81-130. | Numdam | MR | Zbl
and . -[2] On the second cohomology group of a Kähler manifold of positive curvature, Proc. Amer. Math. Soc. 16 (19765), 119-122. | MR | Zbl
and . -[3] Harnack's inequality for elliptic differential equations on minimal surfaces, Inv. Math. 15 (1972), 24-46. | MR | Zbl
and . -[4] Comparison Theorems in Riemannian Geometry, North-Holland Publishing Co., Amsterdam, 1975. | MR | Zbl
and . -[5] The splitting theorem for manifolds of non-negative Ricci curvature, J. Diff. Geom., 6, (1971), 119-128. | MR | Zbl
and . -[6] On the structure of complete manifolds of non-negative curvature, Ann. of Math. 96 (1972), 413-443. | MR | Zbl
and . -[7] Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975), 333-354. | MR | Zbl
and . -[8] Some isoperimetric inequalities and consequences, Ann. Scient. Ec. Norm. Sup. 13 (1980). | Numdam | MR | Zbl
. -[9] Analysis on non-compact Kähler manifolds, Proc. Symp. Pure Math., Vol. 30, Part II, Amer. Math. Soc. (1977). | Zbl
and . -[10] Function Theory on Manifolds which Possess a Pole, Lecture Notes in Math., Vol. 669, Springer-Verlag, Berlin-Heidelberg-New York, 1979. | MR | Zbl
and . -[11] Affine open subsets of algebraic varieties and ample divisors, Ann. of Math. 89 (1969), 160-183. | MR | Zbl
. -[12] L2-estimates and existence theorems for the ∂-operator, Acta. Math. 113 (1965), 89-152. | Zbl
. -[13] Fonctions entières (n variables) et fonctions pluri-sousharmoniques d'ordre fini dans Cn, J. Anal. Math. 12 (1964), 365-407. | MR | Zbl
. -[14] 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 | Zbl
. -[15] Courbure bisectionnelle positive et variétés algébriques affines, Comptes Rendus, Acad. Sc. Paris, Vol. 296, Série A (1983), 473-476. | MR | Zbl
. -[16] 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 | Zbl
. -[17] The Poincaré-Lelong equation on complete Kähler manifolds, Comp. Math., Vol. 44, Fasc. 1-3 (1981), 183-218. | Numdam | MR | Zbl
, and . -[18] On Harnack's theorem for elliptic differential equations, Comm. Pure and Appl. Math., 14 (1961), 577-591. | MR | Zbl
. -[19] A topological characterization of the affine plane as an algebraic variety, Ann. of Math. 94 (1971), 69-88. | MR | Zbl
. -[20] Faisceaux algébriques cohérents, Ann. of Math. 61 (1955), 197-278. | MR | Zbl
. -[21] Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier 6 (1956), 1-42. | Numdam | MR | Zbl
. -[22] Pseudoconvexity and the problem of Levi, Bull. Amer. Math. Soc. 84 (1978), 481-512. | MR | Zbl
. -[23] Analyticity of sets associated to Lelong numbers and the extension of closed positive currents, Invent. Math. 27 (1874), 53-156. | MR | Zbl
. -[24] Complete Kähler manifolds with non-positive curvature of faster than quadratic decay, Ann. Math. 105 (1977), 225-264. | MR | Zbl
and . -[25] 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 | Zbl
. -[26] Equations elliptiques du second ordre à coefficients discontinus, Séminaire de Mathématiques Supérieures 16, 1966. | MR | Zbl
. -[27] The Lelong number in a point of a complex analytic set, Math. Ann. 172 (1967), 269-312. | MR | Zbl
. -[28] Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201-228. | MR | Zbl
. -[29] Le type d'une surface et sa courbure totale, Comment. Math. Helv. 14 (1941-1942), 230-233. | MR | Zbl
and . -[30] On complete open manifolds of non-negative curvature, Ann. of Math. 90 (1969), 75-90. | MR | Zbl
and . -[31] Some results on nonnegatively curved manifolds, J. Diff. Geom. 9 (1974), 583-600. | MR | Zbl
. -[32] An elemetary method in the study of nonnegative curvature, Acta Math. 142 (1979), 57-78. | MR | Zbl
. -- Complete Kähler metrics with positive holomorphic sectional curvatures on certain line bundles (related to a cohomogeneity one point of view on a Yau conjecture), Acta Mathematica Scientia, Volume 44 (2024) no. 1, p. 78 | DOI:10.1007/s10473-024-0103-5
- Existence of nonconstant CR-holomorphic functions of polynomial growth in Sasakian manifolds, Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 0 (2023) no. 0 | DOI:10.1515/crelle-2023-0046
- Three circle theorem on almost Hermitian manifolds and applications, Calculus of Variations and Partial Differential Equations, Volume 61 (2022) no. 5 | DOI:10.1007/s00526-022-02294-5
- Holomorphic Functions on a Class of Kähler Manifolds With Nonnegative Curvature, I, International Mathematics Research Notices, Volume 2022 (2022) no. 4, p. 2615 | DOI:10.1093/imrn/rnaa204
- Cohn–Vossen inequality on certain noncompact Kähler manifolds, Mathematische Zeitschrift, Volume 302 (2022) no. 2, p. 1025 | DOI:10.1007/s00209-022-03105-5
- Compactification of certain Kähler manifolds with nonnegative Ricci curvature, Advances in Mathematics, Volume 382 (2021), p. 107652 | DOI:10.1016/j.aim.2021.107652
- On the Sharp Dimension Estimate of CR Holomorphic Functions in Sasakian Manifolds, International Mathematics Research Notices, Volume 2021 (2021) no. 17, p. 12888 | DOI:10.1093/imrn/rnz164
- Curvature and
Bergman Spaces on Complex Submanifolds in , The Journal of Geometric Analysis, Volume 31 (2021) no. 7, p. 7352 | DOI:10.1007/s12220-020-00529-5 - On the three-circle theorem and its applications in Sasakian manifolds, Calculus of Variations and Partial Differential Equations, Volume 58 (2019) no. 3 | DOI:10.1007/s00526-019-1538-8
- Yau's uniformization conjecture for manifolds with non-maximal volume growth, Acta Mathematica Scientia, Volume 38 (2018) no. 5, p. 1468 | DOI:10.1016/s0252-9602(18)30828-2
- On the CR Poincaré–Lelong Equation, Yamabe Steady Solitons and Structures of Complete Noncompact Sasakian Manifolds, Acta Mathematica Sinica, English Series, Volume 34 (2018) no. 8, p. 1313 | DOI:10.1007/s10114-018-7342-0
- Special birational transformations of type (2,1), Journal of Algebraic Geometry, Volume 27 (2017) no. 1, p. 55 | DOI:10.1090/jag/695
- Gromov-Hausdorff limits of Kähler manifolds and the finite generation conjecture, Annals of Mathematics, Volume 184 (2016) no. 3, p. 775 | DOI:10.4007/annals.2016.184.3.4
- Three-circle theorem and dimension estimate for holomorphic functions on Kähler manifolds, Duke Mathematical Journal, Volume 165 (2016) no. 15 | DOI:10.1215/00127094-3645009
- An Optimal Gap Theorem in a Complete Strictly Pseudoconvex CR
( 2 n + 1 ) -Manifold, The Journal of Geometric Analysis, Volume 26 (2016) no. 3, p. 2425 | DOI:10.1007/s12220-015-9632-4 - Holomorphic functions on Kähler-Ricci solitons, Journal of the London Mathematical Society, Volume 89 (2014) no. 3, p. 817 | DOI:10.1112/jlms/jdt078
- Positively curved complete noncompact Kähler manifolds, Acta Mathematica Scientia, Volume 29 (2009) no. 4, p. 829 | DOI:10.1016/s0252-9602(09)60073-4
- On complete noncompact Kähler manifolds with positive bisectional curvature, Mathematische Annalen, Volume 327 (2003) no. 1, p. 1 | DOI:10.1007/s00208-003-0385-1
- A uniformization theorem for complete Kähler manifolds with positive holomorphic bisectional curvature, The Journal of Geometric Analysis, Volume 8 (1998) no. 1, p. 117 | DOI:10.1007/bf02922111
- Ricci flow and the uniformization on complete noncompact Kähler manifolds, Journal of Differential Geometry, Volume 45 (1997) no. 1 | DOI:10.4310/jdg/1214459756
- Compactification of K�hler manifolds with negative Ricci curvature, Inventiones Mathematicae, Volume 106 (1991) no. 1, p. 13 | DOI:10.1007/bf01243901
- Integrality of characteristic numbers on complete K�hler manifolds, Mathematische Annalen, Volume 289 (1991) no. 1, p. 491 | DOI:10.1007/bf01446585
- On complex manifolds which can be compactified by adding finitely many points, Inventiones Mathematicae, Volume 101 (1990) no. 1, p. 173 | DOI:10.1007/bf01231500
- Compactification of complete Kähler surfaces with negative Ricci curvature, Inventiones Mathematicae, Volume 99 (1990) no. 1, p. 145 | DOI:10.1007/bf01234414
- An embedding theorem of complete Kähler manifolds of positive Ricci curvature onto quasi-projective varieties, Mathematische Annalen, Volume 286 (1990) no. 1-3, p. 373 | DOI:10.1007/bf01453581
- Hyperbolicity of negatively curved K�hler manifolds, Mathematische Annalen, Volume 287 (1990) no. 1, p. 47 | DOI:10.1007/bf01446877
- Topics in Complex Differential Geometry, Recent Topics in Differential and Analytic Geometry (1990), p. 1 | DOI:10.1016/b978-0-12-001018-9.50007-5
- On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth, Inventiones Mathematicae, Volume 97 (1989) no. 2, p. 313 | DOI:10.1007/bf01389045
Cité par 28 documents. Sources : Crossref