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On the existence of parabolic actions in convex domains of $ℂ^{k + 1}$

François Berteloot; Ninh Van Thu — 2015

Czechoslovak Mathematical Journal

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.

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

On the existence of parabolic actions in convex domains of $ℂ^{k + 1}$