The analyticity of -concave sets of locally finite Hausdorff measure
Annales de l'institut Fourier (2000)
- Volume: 50, Issue: 4, page 1191-1203
- ISSN: 0373-0956
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topVâjâitu, Viorel. "The analyticity of $q$-concave sets of locally finite Hausdorff $(2n-2q)$ measure." Annales de l'institut Fourier 50.4 (2000): 1191-1203. <http://eudml.org/doc/75453>.
@article{Vâjâitu2000,
abstract = {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.},
author = {Vâjâitu, Viorel},
journal = {Annales de l'institut Fourier},
keywords = {-convexity; -concavity; Hausdorff measure; analytic set},
language = {eng},
number = {4},
pages = {1191-1203},
publisher = {Association des Annales de l'Institut Fourier},
title = {The analyticity of $q$-concave sets of locally finite Hausdorff $(2n-2q)$ measure},
url = {http://eudml.org/doc/75453},
volume = {50},
year = {2000},
}
TY - JOUR
AU - Vâjâitu, Viorel
TI - The analyticity of $q$-concave sets of locally finite Hausdorff $(2n-2q)$ measure
JO - Annales de l'institut Fourier
PY - 2000
PB - Association des Annales de l'Institut Fourier
VL - 50
IS - 4
SP - 1191
EP - 1203
AB - 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.
LA - eng
KW - -convexity; -concavity; Hausdorff measure; analytic set
UR - http://eudml.org/doc/75453
ER -
References
top- [1] A. ANDREOTTI, H. GRAUERT, Théorèmes de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France, 90 (1962), 193-259. Zbl0106.05501MR27 #343
- [2] E. M. CHIRKA, On the removable singularities for meromorphic mappings, Ann. Polon. Math., 70 (1998), 43-47. Zbl0932.32032
- [3] M. COLŢOIU, n-concavity of n-dimensional complex spaces, Math. Z., 210 (1992), 203-206. Zbl0735.32012MR93f:32016
- [4] M. COLŢOIU, Complete locally pluripolar sets, J. reine angew. Math., 412 (1990), 108-112. Zbl0711.32008MR91h:32010
- [5] J.-P. DEMAILLY, Cohomology of q-convex spaces in top degress, Math. Z., 204 (1990), 283-295. Zbl0682.32017MR91e:32014
- [6] K. DIEDERICH, J.-E. FORNÆSS, Thin complements of complete Kähler domains, Math. Ann., 259 (1982), 331-341. Zbl0469.32003
- [7] K. DIEDERICH, J.-E. FORNÆSS, On the nature of thin complements of complete Kähler domains, Math. Ann., 268 (1984), 475-495. Zbl0527.32012
- [8] K. DIEDERICH, J.-E. FORNÆSS, Smoothing q-convex functions and vanishing theorems, Invent. Math., 82 (1985), 291-305. Zbl0586.32022MR87b:32029
- [9] K. DIEDERICH, J.-E. FORNÆSS, Smoothing q-convex functions in the singular case, Math. Ann., 273 (1986), 665-671. Zbl0586.32023MR87d:32034
- [10] G. DLOUSSKY, Analyticité séparée et prolongement analytique, Math. Ann., 286 (1990), 153-170. Zbl0701.32003MR91i:32005
- [11] H. FEDERER, Geometric measure theory, Berlin-Heidelberg-New York, Springer, 1969. Zbl0176.00801MR41 #1976
- [12] J.-E. FORNÆSS, N. SIBONY, Oka's inequality for currents and applications, Math. Ann., 301 (1995), 399-419. Zbl0832.32010MR96k:32013
- [13] H. GRAUERT, Charakterisierung der Holomorphiegebiete durch die vollständige Kählersche Metrik, Math. Ann., 131 (1965), 38-75. Zbl0073.30203MR17,1072a
- [14] F. HARTOGS, Über die aus der singulären Stellen einer analytischen Funktion mehrerer Veränderlichen bestehende Gebielde, Acta Math., 32 (1909), 57-79. Zbl40.0472.01JFM40.0472.01
- [15] A. HIRSCHOWITZ, Entre les hypersurfaces et les ensembles pseudoconcaves, Ann. Scuola Norm. Sup. Pisa, 27 (1973), 873-887. Zbl0343.32020MR51 #3523
- [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. Zbl0932.32019MR2001a:32015
- [17] B. JOSEFSON, On the equivalence between locally polar and globally polar in ℂn, Arkiv för Mat., 16 (1978), 109-115. Zbl0383.31003MR58 #28669
- [18] T. NISHINO, Sur les ensembles pseudoconcaves, J. Math. Kyoto Univ., 1 (1961/1962), 225-245. Zbl0109.05501MR26 #5184
- [19] T. OHSAWA, Analyticity of complements of complete Kähler domains, Proc. Japan Acad., 56, Ser. A, (1980), 484-487. Zbl0485.32006MR82j:32025
- [20] M. PETERNELL, Continuous q-convex exhaustion functions, Invent. Math., 85 (1986), 249-262. Zbl0599.32016MR87j:32055
- [21] B. SHIFFMAN, On the removal of singularities for analytic sets, The Mich. Math. J., 15-16 (1968/1969), 111-120. Zbl0165.40503MR37 #464
- [22] V. VÂJÂITU, q-completeness and q-concavity of the union of open subspaces, Math. Z., 221 (1996), 217-229. Zbl0844.32014MR97d:32020
- [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. Zbl0923.32013MR98i:32034
- [24] V. VÂJÂITU, Invariance of q-completeness with corners under finite holomorphic surjective maps, Bull. Belg. Math. Soc., 5 (1998), 713-718. Zbl1045.32500MR99j:32018
- [25] V. VÂJÂITU, A Levi problem for continuous strongly q-plurisubharmonic functions, C. R. Acad. Sci. Paris, 328 (1999), 573-578. Zbl0935.31006MR2000a:32021
- [26] J. WERMER, Polynomially convex hull and analyticity, Arkiv för Matem., 20 (1982), 129-135. Zbl0491.32013MR84b:32021
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