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arXiv · 2010.00837

Asymptotic upper bound for tangential speed of parabolic semigroups of holomorphic self-maps in the unit disc

Davide Cordella
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Abstract

We show that the tangential speed of a parabolic semigroup of holomorphic self-maps in the unit disc is asymptotically bounded from above by (1/2)logt, proving a conjecture by Bracci. In order to show the proof we need a result of "asymptotical monotonicity" of the tangential speed for proper pairs of parabolic semigroups with positive hyperbolic step.

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Davide Cordella. 2020-10-02. Asymptotic upper bound for tangential speed of parabolic semigroups of holomorphic self-maps in the unit disc. https://doi.org/10.1007/s10231-021-01100-x

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