no. 4
The analyticity of q-concave sets of locally finite Hausdorff (2n-2q) measure
Annales de l'Institut Fourier, Tome 50 (2000) no. 4, pp. 1191-1203.

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.

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     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},
     pages = {1191--1203},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {50},
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     year = {2000},
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Vâjâitu, Viorel. The analyticity of $q$-concave sets of locally finite Hausdorff $(2n-2q)$ measure. Annales de l'Institut Fourier, Tome 50 (2000) no. 4, pp. 1191-1203. doi : 10.5802/aif.1789. https://aif.centre-mersenne.org/articles/10.5802/aif.1789/

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

[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 | Zbl

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

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

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

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

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

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

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

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

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

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

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

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

[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 | Zbl

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

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

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

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

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

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

[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 | Zbl

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

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

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

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