Resonances in Loewner equations

Details Resonances in Loewner equations Resonances in Loewner equations

2010-06-15

arxiv.org/abs/1006.2989v2

Mathematics

Complex Variables

23 pages, corrected typos, revised argument in Proposition 5.5, result unchanged

Scientific paper

10.1016/j.aim.2011.03.010

We prove that given a Herglotz vector field on the unit ball of
$\mathbb{C}^n$ of the form $H(z,t)=(a_1 z_1,...,a_n z_n)+O(|z|^2)$ with $\Re
a_j<0$ for all $j$, its evolution family admits an associated Loewner chain,
which is normal if no real resonances occur. Hence the Loewner-Kufarev PDE
admits a solution defined for all positive times.

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