2000 character limit reached
Resonances in Loewner equations (1006.2989v2)
Published 15 Jun 2010 in math.CV and math.DS
Abstract: 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.