Regularization of currents and entropy

Tien-Cuong Dinh; Nessim Sibony

Annales scientifiques de l'École Normale Supérieure (2004)

  • Volume: 37, Issue: 6, page 959-971
  • ISSN: 0012-9593

How to cite

top

Dinh, Tien-Cuong, and Sibony, Nessim. "Regularization of currents and entropy." Annales scientifiques de l'École Normale Supérieure 37.6 (2004): 959-971. <http://eudml.org/doc/82650>.

@article{Dinh2004,
author = {Dinh, Tien-Cuong, Sibony, Nessim},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {-current; Kähler manifold; weak convergence; pluriharmanic current; bounded potential},
language = {eng},
number = {6},
pages = {959-971},
publisher = {Elsevier},
title = {Regularization of currents and entropy},
url = {http://eudml.org/doc/82650},
volume = {37},
year = {2004},
}

TY - JOUR
AU - Dinh, Tien-Cuong
AU - Sibony, Nessim
TI - Regularization of currents and entropy
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2004
PB - Elsevier
VL - 37
IS - 6
SP - 959
EP - 971
LA - eng
KW - -current; Kähler manifold; weak convergence; pluriharmanic current; bounded potential
UR - http://eudml.org/doc/82650
ER -

References

top
  1. [1] Alessandrini L., Bassanelli G., Plurisubharmonic currents and their extension across analytic subsets, Forum Math.5 (6) (1993) 577-602. Zbl0784.32014MR1242890
  2. [2] Bassanelli G., A cut-off theorem for plurisubharmonic currents, Forum Math.6 (5) (1994) 567-595. Zbl0808.32010MR1295153
  3. [3] Berndtsson B., Sibony N., The ¯ equation on a positive current, Invent. Math.147 (2002) 371-428. Zbl1031.32005MR1881924
  4. [4] Blanchard A., Sur les variétés analytiques complexes, Ann. Sci. Éc. Norm. Sup. (3)73 (1956) 157-202. Zbl0073.37503MR87184
  5. [5] Bowen R., Topological entropy for noncompact sets, Trans. Amer. Math. Soc.184 (1973) 125-136. Zbl0274.54030MR338317
  6. [6] Demailly J.-P., Monge–Ampère operators, Lelong numbers and intersection theory, in: Ancona V., Silva A. (Eds.), Complex Analysis and Geometry, Plenum Press, 1993, pp. 115-193. Zbl0792.32006MR1211880
  7. [7] Demailly J.-P., Pseudoconvex-concave duality and regularization of currents, in: Several Complex Variables (Berkeley, CA, 1995–1996), Math. Sci. Res. Inst. Publ., vol. 37, Cambridge Univ. Press, Cambridge, 1999, pp. 233-271. Zbl0960.32011MR1748605
  8. [8] Dinh T.C., Distribution des préimages et des points périodiques d'une correspondance polynomiale, Bull. Soc. Math. France, in press. Zbl1090.37032
  9. [9] Dinh T.C., Lawrence M., Polynomial hull and positive currents, Ann. Fac. Sci. ToulouseXII (3) (2003) 317-334. Zbl1065.32004MR2030090
  10. [10] Dinh T.C., Sibony N., Une borne supérieure pour l'entropie topologique d'une application rationnelle, Ann. of Math., in press. Zbl1084.54013
  11. [11] Dinh T.C., Sibony N., Distribution des valeurs de transformations méromorphes et applications, preprint, 2003, math.DS/0306095. MR2208805
  12. [12] Dinh T.C., Sibony N., Green currents for automorphisms of compact Kähler manifolds, JAMS, in press. Zbl1066.32024
  13. [13] Duval J., Sibony N., Polynomial convexity, rational convexity, and currents, Duke Math. J.79 (2) (1995) 487-513. Zbl0838.32006MR1344768
  14. [14] Fornæss J.E., Sibony N., Harmonic currents with finite energy, preprint, 2004, math.CV/0402432. 
  15. [15] Friedland S., Entropy of polynomial and rational maps, Ann. of Math.133 (1991) 359-368. Zbl0737.54006MR1097242
  16. [16] Gromov M., On the entropy of holomorphic maps, in: Séminaire Bourbaki, vol. 1985/86, Astérique, vols. 145–146, Soc. Math. France, 1987, pp. 225-240. Zbl0611.58041MR880035
  17. [17] Gromov M., On the entropy of holomorphic maps, Enseign. Math.49 (2003) 217-235, Manuscript (1977). Zbl1080.37051MR2026895
  18. [18] Lelong P., Fonctions plurisousharmoniques et formes différentielles positives, Dunod, Paris, 1968. Zbl0192.20103MR243112
  19. [19] Méo M., Image inverse d'un courant positif fermé par une application surjective, CRAS322 (1996) 1141-1144. Zbl0858.32012MR1396655
  20. [20] Sibony N., Dynamique des applications rationnelles de P k , Panoramas et Synthèses8 (1999) 97-185. Zbl1020.37026MR1760844
  21. [21] Sibony N., Quelques problèmes de prolongement de courants en analyse complexe, Duke Math. J.52 (1) (1985) 157-197. Zbl0578.32023MR791297
  22. [22] Skoda H., Prolongement des courants positifs, fermés de masse finie, Invent. Math.66 (1982) 361-376. Zbl0488.58002MR662596
  23. [23] Yomdin Y., Volume growth and entropy, Israel J. Math.57 (1987) 285-300. Zbl0641.54036MR889979

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.