Asymptotics of the translation flow on holomorphic maps out of the poly-plane

Gekhtman, Dmitri

doi:10.1090/ecgd/330

Asymptotics of the translation flow on holomorphic maps out of the poly-plane
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by Dmitri Gekhtman

Conform. Geom. Dyn. 23 (2019), 1-16

DOI: https://doi.org/10.1090/ecgd/330

Published electronically: February 4, 2019

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Abstract:

We study the family of holomorphic maps from the polydisk to the disk which restrict to the identity on the diagonal. In particular, we analyze the asymptotics of the orbit of such a map under the conjugation action of a unipotent subgroup of $\operatorname {PSL}_2(\mathbb {R})$. We discuss an application of our results to the study of the Carathéodory metric on Teichmüller space.

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