The analyticity of q -concave sets of locally finite Hausdorff ( 2 n - 2 q ) measure

Viorel Vâjâitu

Annales de l'institut Fourier (2000)

  • Volume: 50, Issue: 4, page 1191-1203
  • ISSN: 0373-0956

Abstract

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

How to cite

top

Vâjâitu, 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. [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. [2] E. M. CHIRKA, On the removable singularities for meromorphic mappings, Ann. Polon. Math., 70 (1998), 43-47. Zbl0932.32032
  3. [3] M. COLŢOIU, n-concavity of n-dimensional complex spaces, Math. Z., 210 (1992), 203-206. Zbl0735.32012MR93f:32016
  4. [4] M. COLŢOIU, Complete locally pluripolar sets, J. reine angew. Math., 412 (1990), 108-112. Zbl0711.32008MR91h:32010
  5. [5] J.-P. DEMAILLY, Cohomology of q-convex spaces in top degress, Math. Z., 204 (1990), 283-295. Zbl0682.32017MR91e:32014
  6. [6] K. DIEDERICH, J.-E. FORNÆSS, Thin complements of complete Kähler domains, Math. Ann., 259 (1982), 331-341. Zbl0469.32003
  7. [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. [8] K. DIEDERICH, J.-E. FORNÆSS, Smoothing q-convex functions and vanishing theorems, Invent. Math., 82 (1985), 291-305. Zbl0586.32022MR87b:32029
  9. [9] K. DIEDERICH, J.-E. FORNÆSS, Smoothing q-convex functions in the singular case, Math. Ann., 273 (1986), 665-671. Zbl0586.32023MR87d:32034
  10. [10] G. DLOUSSKY, Analyticité séparée et prolongement analytique, Math. Ann., 286 (1990), 153-170. Zbl0701.32003MR91i:32005
  11. [11] H. FEDERER, Geometric measure theory, Berlin-Heidelberg-New York, Springer, 1969. Zbl0176.00801MR41 #1976
  12. [12] J.-E. FORNÆSS, N. SIBONY, Oka's inequality for currents and applications, Math. Ann., 301 (1995), 399-419. Zbl0832.32010MR96k:32013
  13. [13] H. GRAUERT, Charakterisierung der Holomorphiegebiete durch die vollständige Kählersche Metrik, Math. Ann., 131 (1965), 38-75. Zbl0073.30203MR17,1072a
  14. [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. [15] A. HIRSCHOWITZ, Entre les hypersurfaces et les ensembles pseudoconcaves, Ann. Scuola Norm. Sup. Pisa, 27 (1973), 873-887. Zbl0343.32020MR51 #3523
  16. [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. [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. [18] T. NISHINO, Sur les ensembles pseudoconcaves, J. Math. Kyoto Univ., 1 (1961/1962), 225-245. Zbl0109.05501MR26 #5184
  19. [19] T. OHSAWA, Analyticity of complements of complete Kähler domains, Proc. Japan Acad., 56, Ser. A, (1980), 484-487. Zbl0485.32006MR82j:32025
  20. [20] M. PETERNELL, Continuous q-convex exhaustion functions, Invent. Math., 85 (1986), 249-262. Zbl0599.32016MR87j:32055
  21. [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. [22] V. VÂJÂITU, q-completeness and q-concavity of the union of open subspaces, Math. Z., 221 (1996), 217-229. Zbl0844.32014MR97d:32020
  23. [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. [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. [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. [26] J. WERMER, Polynomially convex hull and analyticity, Arkiv för Matem., 20 (1982), 129-135. Zbl0491.32013MR84b:32021

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.