A Wong-Rosay type theorem for proper holomorphic self-maps

Emmanuel Opshtein[1]

  • [1] Institut de Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, 7 rue René Descartes, 67000 Strasbourg, France.

Annales de la faculté des sciences de Toulouse Mathématiques (2010)

  • Volume: 19, Issue: 3-4, page 513-524
  • ISSN: 0240-2963

Abstract

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In this short paper, we show that the only proper holomorphic self-maps of bounded domains in ℂ k whose iterates approach a strictly pseudoconvex point of the boundary are automorphisms of the euclidean ball. This is a Wong-Rosay type theorem for a sequence of maps whose degrees are a priori unbounded.

How to cite

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Opshtein, Emmanuel. "A Wong-Rosay type theorem for proper holomorphic self-maps." Annales de la faculté des sciences de Toulouse Mathématiques 19.3-4 (2010): 513-524. <http://eudml.org/doc/115854>.

@article{Opshtein2010,
abstract = {In this short paper, we show that the only proper holomorphic self-maps of bounded domains in $\mathbb\{C\}^k$ whose iterates approach a strictly pseudoconvex point of the boundary are automorphisms of the euclidean ball. This is a Wong-Rosay type theorem for a sequence of maps whose degrees are a priori unbounded.},
affiliation = {Institut de Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, 7 rue René Descartes, 67000 Strasbourg, France.},
author = {Opshtein, Emmanuel},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {proper holomorphic mapping; automorphism group},
language = {eng},
number = {3-4},
pages = {513-524},
publisher = {Université Paul Sabatier, Toulouse},
title = {A Wong-Rosay type theorem for proper holomorphic self-maps},
url = {http://eudml.org/doc/115854},
volume = {19},
year = {2010},
}

TY - JOUR
AU - Opshtein, Emmanuel
TI - A Wong-Rosay type theorem for proper holomorphic self-maps
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2010
PB - Université Paul Sabatier, Toulouse
VL - 19
IS - 3-4
SP - 513
EP - 524
AB - In this short paper, we show that the only proper holomorphic self-maps of bounded domains in $\mathbb{C}^k$ whose iterates approach a strictly pseudoconvex point of the boundary are automorphisms of the euclidean ball. This is a Wong-Rosay type theorem for a sequence of maps whose degrees are a priori unbounded.
LA - eng
KW - proper holomorphic mapping; automorphism group
UR - http://eudml.org/doc/115854
ER -

References

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  1. Alexander (H.).— Holomorphic mappings from the ball and polydisc. Math. Ann., 209:249-256 (1974). Zbl0272.32006MR352531
  2. Bell (S.).— Local boundary behavior of proper holomorphic mappings. In Complex analysis of several variables (Madison, Wis., 1982), volume 41 of Proc. Sympos. Pure Math., p. 1-7. Amer. Math. Soc., Providence, RI (1984). Zbl0537.32005MR740867
  3. Berteloot (F.).— Attraction des disques analytiques et continuité höldérienne d’applications holomorphes propres. In Topics in complex analysis (Warsaw, 1992), volume 31 of Banach Center Publ., p. 91-98. Polish Acad. Sci., Warsaw (1995). Zbl0831.32012MR1341379
  4. Boggess (A.).— CR manifolds and the tangential Cauchy-Riemann complex. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL (1991). Zbl0760.32001MR1211412
  5. Fornaess (J. E.).— Biholomorphic mappings between weakly pseudoconvex domains. Pacific J. Math., 74(1):63-65 (1978). Zbl0353.32026MR481111
  6. MacCluer (B. D.).— Iterates of holomorphic self-maps of the unit ball in C N . Michigan Math. J., 30(1):97-106 (1983). Zbl0528.32019MR694933
  7. Nagel (A.), Stein (E. M.), and Wainger (S.).— Balls and metrics defined by vector fields. I. Basic properties. Acta Math., 155(1-2):103-147 (1985). Zbl0578.32044MR793239
  8. Opshtein (E.).— Sphericity and contractibility of strictly pseudoconvex hypersurfaces. Prepublication, arXiv math.CV/0504054 (2005). 
  9. Opshtein (E.).— Dynamique des applications holomorphes propres des domaines réguliers et problème de l’injectivité. Math. Ann., 133(1):1-30 (2006). Zbl1097.32008MR2217682
  10. Ourimi (N.).— Some compactness theorems of families of proper holomorphic correspondences. Publ. Mat., 47(1):31-43 (2003). Zbl1044.32012MR1970893
  11. Pinčuk (S. I.).— The analytic continuation of holomorphic mappings. Mat. Sb. (N.S.), 98(140)(3(11)):416-435, 495-496 (1975). Zbl0366.32010MR393562
  12. Rosay (J.-P.).— Sur une caractérisation de la boule parmi les domaines de C n par son groupe d’automorphismes. Ann. Inst. Fourier (Grenoble), 29(4):ix, p. 91-97 (1979). Zbl0402.32001MR558590
  13. Rudin (W.).— Function theory in the unit ball of C n , volume 241 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science]. Springer-Verlag, New York (1980). Zbl0495.32001MR601594
  14. Tumanov (A. E.) and Khenkin (G. M.).— Local characterization of holomorphic automorphisms of Siegel domains. Funktsional. Anal. i Prilozhen., 17(4):49-61 (1983). Zbl0572.32018MR725415
  15. Webster (S. M.).— On the transformation group of a real hypersurface. Trans. Amer. Math. Soc., 231(1):179-190 (1977). Zbl0368.57013MR481085
  16. Wong (B.).— Characterization of the unit ball in C n by its automorphism group. Invent. Math., 41(3):253-257 (1977). Zbl0385.32016MR492401

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