Geodesic
On the existence of parabolic actions in convex domains of $\mathbb C^{k+1}$
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 3, pp. 579-585
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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.
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.
DOI : 10.1007/s10587-015-0197-y
Classification : 32H02, 32H50, 32M05
Keywords: parabolic boundary point; convex domain; automorphism group 
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Berteloot, François; Thu, Ninh Van. On the existence of parabolic actions in convex domains of $\mathbb C^{k+1}$. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 3, pp. 579-585. doi: 10.1007/s10587-015-0197-y

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