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

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

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

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.02.038
Marinescu, George 1, 2; Dinh, Tien-Cuong 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
@article{CRMATH_2006__342_9_675_0,
     author = {Marinescu, George and Dinh, Tien-Cuong},
     title = {On the compactification of hyperconcave ends},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {675--680},
     publisher = {Elsevier},
     volume = {342},
     number = {9},
     year = {2006},
     doi = {10.1016/j.crma.2006.02.038},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.crma.2006.02.038/}
}
TY  - JOUR
AU  - Marinescu, George
AU  - Dinh, Tien-Cuong
TI  - On the compactification of hyperconcave ends
JO  - Comptes Rendus. Mathématique
PY  - 2006
SP  - 675
EP  - 680
VL  - 342
IS  - 9
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.crma.2006.02.038/
DO  - 10.1016/j.crma.2006.02.038
LA  - en
ID  - CRMATH_2006__342_9_675_0
ER  - 
%0 Journal Article
%A Marinescu, George
%A Dinh, Tien-Cuong
%T On the compactification of hyperconcave ends
%J Comptes Rendus. Mathématique
%D 2006
%P 675-680
%V 342
%N 9
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.crma.2006.02.038/
%R 10.1016/j.crma.2006.02.038
%G en
%F CRMATH_2006__342_9_675_0
Marinescu, George; Dinh, Tien-Cuong. 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. http://archive.numdam.org/articles/10.1016/j.crma.2006.02.038/

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

[2] Andreotti, A.; Tomassini, G. Some remarks on pseudoconcave manifolds (Haeflinger, A.; Narasimhan, R., 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] Colţoiu, M.; Mihalache, N. Strongly plurisubharmonic exhaustion functions on 1-convex spaces, Math. Ann., Volume 270 (1985), pp. 63-68

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

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

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

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

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

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

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

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

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

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

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

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

Cited by Sources: