The analyticity of q-concave sets of locally finite Hausdorff (2n-2q) measure
Vâjâitu, Viorel
Annales de l'Institut Fourier, Tome 50 (2000), p. 1191-1203 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

Nous montrons l’analyticité d’un ensemble q-concave contenu dans un espace complexe de dimension n et de (2n-2q)-mesure de Hausdorff localement finie. On en déduit un théorème d’élimination des singularités pour les applications méromorphes à valeurs dans un espace q-complet.

We prove the analyticity of q-concave sets of locally finite Hausdorff (2n-2q)-measure in a n-dimensional complex space. We apply it to give a removability criterion for meromorphic maps with values in q-complete spaces.

@article{AIF_2000__50_4_1191_0,
     author = {V\^aj\^aitu, Viorel},
     title = {The analyticity of $q$-concave sets of locally finite Hausdorff $(2n-2q)$ measure},
     journal = {Annales de l'Institut Fourier},
     volume = {50},
     year = {2000},
     pages = {1191-1203},
     doi = {10.5802/aif.1789},
     mrnumber = {2001j:32010},
     zbl = {0974.32006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2000__50_4_1191_0}
}

Vâjâitu, Viorel. The analyticity of $q$-concave sets of locally finite Hausdorff $(2n-2q)$ measure. Annales de l'Institut Fourier, Tome 50 (2000) pp. 1191-1203. doi : 10.5802/aif.1789. http://gdmltest.u-ga.fr/item/AIF_2000__50_4_1191_0/

[1] A. Andreotti, H. Grauert, Théorèmes de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France, 90 (1962), 193-259. | Numdam | MR 27 #343 | Zbl 0106.05501

[2] E. M. Chirka, On the removable singularities for meromorphic mappings, Ann. Polon. Math., 70 (1998), 43-47.

[3] M. Colţoiu, n-concavity of n-dimensional complex spaces, Math. Z., 210 (1992), 203-206. | MR 93f:32016 | Zbl 0782.32011

[4] M. Colţoiu, Complete locally pluripolar sets, J. reine angew. Math., 412 (1990), 108-112. | MR 91h:32010 | Zbl 0711.32008

[5] J.-P. Demailly, Cohomology of q-convex spaces in top degress, Math. Z., 204 (1990), 283-295. | MR 91e:32014 | Zbl 0682.32017

[6] K. Diederich, J.-E. Fornæss, Thin complements of complete Kähler domains, Math. Ann., 259 (1982), 331-341. | Zbl 0476.32011

[7] K. Diederich, J.-E. Fornæss, On the nature of thin complements of complete Kähler domains, Math. Ann., 268 (1984), 475-495. | Zbl 0527.32012

[8] K. Diederich, J.-E. Fornæss, Smoothing q-convex functions and vanishing theorems, Invent. Math., 82 (1985), 291-305. | MR 87b:32029 | Zbl 0586.32022

[9] K. Diederich, J.-E. Fornæss, Smoothing q-convex functions in the singular case, Math. Ann., 273 (1986), 665-671. | MR 87d:32034 | Zbl 0586.32023

[10] G. Dloussky, Analyticité séparée et prolongement analytique, Math. Ann., 286 (1990), 153-170. | MR 91i:32005 | Zbl 0701.32003

[11] H. Federer, Geometric measure theory, Berlin-Heidelberg-New York, Springer, 1969. | MR 41 #1976 | Zbl 0176.00801

[12] J.-E. Fornæss, N. Sibony, Oka's inequality for currents and applications, Math. Ann., 301 (1995), 399-419. | MR 96k:32013 | Zbl 0832.32010

[13] H. Grauert, Charakterisierung der Holomorphiegebiete durch die vollständige Kählersche Metrik, Math. Ann., 131 (1965), 38-75. | MR 17,1072a | Zbl 0073.30203

[14] F. Hartogs, Über die aus der singulären Stellen einer analytischen Funktion mehrerer Veränderlichen bestehende Gebielde, Acta Math., 32 (1909), 57-79. | JFM 40.0472.01

[15] A. Hirschowitz, Entre les hypersurfaces et les ensembles pseudoconcaves, Ann. Scuola Norm. Sup. Pisa, 27 (1973), 873-887. | Numdam | MR 51 #3523 | Zbl 0343.32020

[16] S. Ivashkovich, A. Silva, The Hartogs type extension theorem for meromorphic mappings into q-complete complex spaces, Boll. U.M.I., (8) 2-B (1999), 251-261. | MR 2001a:32015 | Zbl 0932.32019

[17] B. Josefson, On the equivalence between locally polar and globally polar in ℂn, Arkiv för Mat., 16 (1978), 109-115. | MR 58 #28669 | Zbl 0383.31003

[18] T. Nishino, Sur les ensembles pseudoconcaves, J. Math. Kyoto Univ., 1 (1961/1962), 225-245. | MR 26 #5184 | Zbl 0109.05501

[19] T. Ohsawa, Analyticity of complements of complete Kähler domains, Proc. Japan Acad., 56, Ser. A, (1980), 484-487. | MR 82j:32025 | Zbl 0485.32006

[20] M. Peternell, Continuous q-convex exhaustion functions, Invent. Math., 85 (1986), 249-262. | MR 87j:32055 | Zbl 0599.32016

[21] B. Shiffman, On the removal of singularities for analytic sets, The Mich. Math. J., 15-16 (1968/1969), 111-120. | MR 37 #464 | Zbl 0165.40503

[22] V. Vâjâitu, q-completeness and q-concavity of the union of open subspaces, Math. Z., 221 (1996), 217-229. | MR 97d:32020 | Zbl 0844.32014

[23] V. Vâjâitu, On P-complete morphisms of complex spaces, Geometric Complex Analysis, Proc. the third International Research Institute, Math. Soc. Japan, Hayama 1995; Eds. J. Noguchi, H. Fujimoto, J. Kajiwara, and T. Ohsawa, pag. 653-665. | MR 98i:32034 | Zbl 0923.32013

[24] V. Vâjâitu, Invariance of q-completeness with corners under finite holomorphic surjective maps, Bull. Belg. Math. Soc., 5 (1998), 713-718. | MR 99j:32018 | Zbl 01266799

[25] V. Vâjâitu, A Levi problem for continuous strongly q-plurisubharmonic functions, C. R. Acad. Sci. Paris, 328 (1999), 573-578. | MR 2000a:32021 | Zbl 0935.31006

[26] J. Wermer, Polynomially convex hull and analyticity, Arkiv för Matem., 20 (1982), 129-135. | MR 84b:32021 | Zbl 0491.32013