On the existence of parabolic actions in convex domains of ℂ k + 1

François Berteloot; Ninh Van Thu

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 3, page 579-585
  • ISSN: 0011-4642

Abstract

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We prove that the one-parameter group of holomorphic automorphisms induced on a strictly geometrically bounded domain by a biholomorphism with a model domain is parabolic. This result is related to the Greene-Krantz conjecture and more generally to the classification of domains having a non compact automorphisms group. The proof relies on elementary estimates on the Kobayashi pseudo-metric.

How to cite

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Berteloot, François, and Thu, Ninh Van. "On the existence of parabolic actions in convex domains of $\mathbb {C}^{k+1}$." Czechoslovak Mathematical Journal 65.3 (2015): 579-585. <http://eudml.org/doc/271806>.

@article{Berteloot2015,
abstract = {We prove that the one-parameter group of holomorphic automorphisms induced on a strictly geometrically bounded domain by a biholomorphism with a model domain is parabolic. This result is related to the Greene-Krantz conjecture and more generally to the classification of domains having a non compact automorphisms group. The proof relies on elementary estimates on the Kobayashi pseudo-metric.},
author = {Berteloot, François, Thu, Ninh Van},
journal = {Czechoslovak Mathematical Journal},
keywords = {parabolic boundary point; convex domain; automorphism group},
language = {eng},
number = {3},
pages = {579-585},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the existence of parabolic actions in convex domains of $\mathbb \{C\}^\{k+1\}$},
url = {http://eudml.org/doc/271806},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Berteloot, François
AU - Thu, Ninh Van
TI - On the existence of parabolic actions in convex domains of $\mathbb {C}^{k+1}$
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 3
SP - 579
EP - 585
AB - We prove that the one-parameter group of holomorphic automorphisms induced on a strictly geometrically bounded domain by a biholomorphism with a model domain is parabolic. This result is related to the Greene-Krantz conjecture and more generally to the classification of domains having a non compact automorphisms group. The proof relies on elementary estimates on the Kobayashi pseudo-metric.
LA - eng
KW - parabolic boundary point; convex domain; automorphism group
UR - http://eudml.org/doc/271806
ER -

References

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