Comptes Rendus
Analytic Geometry
On the compactification of hyperconcave ends
[Compactification de bouts hyperconcaves]
Comptes Rendus. Mathématique, Volume 342 (2006) no. 9, pp. 675-680.

On étudie une classe de variétés dont les bouts strictement pseudoconcaves peuvent être compactifiés, même en dimension deux.

We find a class of manifolds whose ‘pseudoconcave holes’ can be filled in, even in dimension two.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.02.038

George Marinescu 1, 2 ; Tien-Cuong Dinh 3

1 Fachbereich Mathematik, Johann Wolfgang Goethe-Universität, 60054, Frankfurt am Main, Germany
2 Institute of Mathematics of the Romanian Academy, Bucharest, Romania
3 Analyse complexe, Institut de mathématiques de Jussieu (UMR 7586 du CNRS), Université Pierre et Marie Curie, 175, rue du Chevaleret, plateau 7D, 75013 Paris cedex, France
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George Marinescu; Tien-Cuong Dinh. On the compactification of hyperconcave ends. Comptes Rendus. Mathématique, Volume 342 (2006) no. 9, pp. 675-680. doi : 10.1016/j.crma.2006.02.038. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.02.038/

[1] A. Andreotti; Y.T. Siu Projective embeddings of pseudoconcave spaces, Ann. Sc. Norm. Sup. Pisa, Volume 24 (1970), pp. 231-278

[2] A. Andreotti; G. Tomassini Some remarks on pseudoconcave manifolds (A. Haeflinger; R. Narasimhan, eds.), Essays on Topology and Related Topics dedicated to G. de Rham, Springer-Verlag, 1970, pp. 85-104

[3] B. Berndtsson, A simple proof of an L2-estimate for ¯ on complete Kähler manifolds, Preprint, 1992

[4] M. Colţoiu; N. Mihalache Strongly plurisubharmonic exhaustion functions on 1-convex spaces, Math. Ann., Volume 270 (1985), pp. 63-68

[5] J.-P. Demailly L2 vanishing theorems for positive line bundles and adjunction theory, Transcendental Methods in Algebraic Geometry, Cetraro, 1994, Lecture Notes in Math., vol. 1646, Springer, Berlin, 1996, pp. 1-97

[6] P. Dolbeault; G. Henkin Chaînes holomorphes à bord donné dans CPn, Bull. Soc. Math. France, Volume 125 (1997), pp. 383-445

[7] G.B. Folland; J.J. Kohn The Neumann Problem for the Cauchy–Riemann Complex, Ann. Math. Stud., vol. 75, Princeton University Press, New York, 1972

[8] H. Grauert Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann., Volume 146 (1962), pp. 331-368

[9] H. Grauert Theory of q-convexity and q-concavity (H. Grauert; Th. Peternell; R. Remmert, eds.), Several Complex Variables VII, Encyclopedia Math. Sci., vol. 74, Springer-Verlag, 1994

[10] L. Hörmander L2-estimates and existence theorem for the ¯-operator, Acta Math., Volume 113 (1965), pp. 89-152

[11] G. Marinescu; T.-C. Dinh On the compactification of hyperconcave ends and the theorems of Siu–Yau and Nadel, 2002 (Invent. Math., in press. Preprint available at) | arXiv

[12] G. Marinescu; N. Yeganefar Embeddability of some strongly pseudoconvex CR manifolds, 2004 (Trans. Amer. Math. Soc., in press. Preprint available at) | arXiv

[13] N. Mok Compactification of complete Kähler–Einstein manifolds of finite volume, Recent Developments in Geometry, Comtemp. Math., vol. 101, Amer. Math. Soc., 1989, pp. 287-301

[14] A. Nadel On complex manifolds which can be compactified by adding finitely many points, Invent. Math., Volume 101 (1990) no. 1, pp. 173-189

[15] A. Nadel; H. Tsuji Compactification of complete Kähler manifolds of negative Ricci curvature, J. Differential Geom., Volume 28 (1988) no. 3, pp. 503-512

[16] H. Rossi Attaching analytic spaces to an analytic space along a pseudoconcave boundary, Proc. Conf. Complex Manifolds (Minneapolis), Springer-Verlag, New York, 1965, pp. 242-256

[17] Y.T. Siu The Fujita conjecture and the extension theorem of Ohsawa–Takegoshi (J. Noguchi et al., eds.), Geometric Complex Analysis, World Scientific Publishing Co., 1996, pp. 577-592

[18] Y.T. Siu; S.T. Yau Compactification of negatively curved complete Kähler manifolds of finite volume, Ann. Math. Stud., vol. 102, Princeton University Press, 1982, pp. 363-380

[19] J. Wermer The hull of a curve in Cn, Ann. of Math., Volume 68 (1958), pp. 45-71

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