Hölder continuity of proper holomorphic mappings

François Berteloot

Studia Mathematica (1991)

  • Volume: 100, Issue: 3, page 229-235
  • ISSN: 0039-3223

Abstract

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We prove the Hölder continuity for proper holomorphic mappings onto certain piecewise smooth pseudoconvex domains with "good" plurisubharmonic peak functions at each point of their boundaries. We directly obtain a quite precise estimate for the exponent from an attraction property for analytic disks. Moreover, this way does not require any consideration of infinitesimal metric.

How to cite

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Berteloot, François. "Hölder continuity of proper holomorphic mappings." Studia Mathematica 100.3 (1991): 229-235. <http://eudml.org/doc/215885>.

@article{Berteloot1991,
abstract = {We prove the Hölder continuity for proper holomorphic mappings onto certain piecewise smooth pseudoconvex domains with "good" plurisubharmonic peak functions at each point of their boundaries. We directly obtain a quite precise estimate for the exponent from an attraction property for analytic disks. Moreover, this way does not require any consideration of infinitesimal metric.},
author = {Berteloot, François},
journal = {Studia Mathematica},
keywords = {proper holomorphic mappings; Hölder continuity; plurisubharmonic peak functions; proper holomorphic maps; piecewise smooth domains},
language = {eng},
number = {3},
pages = {229-235},
title = {Hölder continuity of proper holomorphic mappings},
url = {http://eudml.org/doc/215885},
volume = {100},
year = {1991},
}

TY - JOUR
AU - Berteloot, François
TI - Hölder continuity of proper holomorphic mappings
JO - Studia Mathematica
PY - 1991
VL - 100
IS - 3
SP - 229
EP - 235
AB - We prove the Hölder continuity for proper holomorphic mappings onto certain piecewise smooth pseudoconvex domains with "good" plurisubharmonic peak functions at each point of their boundaries. We directly obtain a quite precise estimate for the exponent from an attraction property for analytic disks. Moreover, this way does not require any consideration of infinitesimal metric.
LA - eng
KW - proper holomorphic mappings; Hölder continuity; plurisubharmonic peak functions; proper holomorphic maps; piecewise smooth domains
UR - http://eudml.org/doc/215885
ER -

References

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  1. [1] H. Alexander, Proper holomorphic mappings in C n , Indiana Univ. Math. J. 26 (1977), 137-146. Zbl0391.32015
  2. [2] E. Bedford and J. E. Fornæ ss, Biholomorphic maps of weakly pseudoconvex domains, Duke Math. J. 45 (1978), 711-749. 
  3. [3] K. Diederich and J. E. Fornæ ss, Pseudoconvex domains: bounded strictly plurisubharmonic exhaustion functions, Invent. Math. 39 (1977), 129-141. Zbl0353.32025
  4. [4] K. Diederich and J. E. Fornæ ss, Proper holomorphic maps onto pseudoconvex domains with real-analytic boundary, Ann. of Math. (2) 110 (1979), 575-592. Zbl0394.32012
  5. [5] F. Forstneric and J.-P. Rosay, Localization of the Kobayashi metric and the boundary continuity of proper holomorphic mappings, Math. Ann. 279 (1987), 239-252. Zbl0644.32013
  6. [6] J. E. Fornæ ss and N. Sibony, Construction of p.s.h. functions on weakly pseudoconvex domains, Duke Math. J. 58 (1989), 633-655. 
  7. [7] J. E. Fornæ ss and B. Stensønes, Lectures on Counterexamples in Several Complex Variables, Math. Notes 33, Princeton Univ. Press, 1987. 
  8. [8] G. M. Henkin, An analytic polyhedron is not holomorphically equivalent to a strictly pseudoconvex domain, Soviet. Math. Dokl. 14 (1973), 858-862. Zbl0288.32015
  9. [9] M. Hervé, Les fonctions analytiques, Presses Univ. de France, 1982. 
  10. [10] G. A. Margulis, Boundary correspondence under biholomorphic mappings of multivariate domains, in: Abstracts of the All-Union Conf. on the Theory of Functions of Several Complex Variables, Kharkov 1971, 137-138. 
  11. [11] S. I. Pinchuk, Holomorphic maps in C n and the problem of holomorphic equivalence, in: Several Complex Variables, Encyclopaedia Math. Sci. 19, Springer, 1989, 173-201. 
  12. [12] R. M. Range, On the topological extension to the boundary of biholomorphic maps in C n , Trans. Amer. Math. Soc. 216 (1976), 203-216. Zbl0313.32034
  13. [13] N. Vormoor, Topologische Fortsetzung biholomorpher Funktionen auf dem Rande bei beschränkten streng-pseudokonvexen Gebieten im C n mit C ∞ -Rand, Math. Ann. 204 (1973), 239-261. Zbl0259.32006

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