We prove that given a Herglotz vector field on the unit ball of C^n of the form H(z,t)=(a_1 z_1,dots,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.
Arosio, L. (2011). Resonances in Loewner equations. ADVANCES IN MATHEMATICS, 227(4), 1413-1435 [10.1016/j.aim.2011.03.010].
Resonances in Loewner equations
AROSIO, LEANDRO
2011-01-01
Abstract
We prove that given a Herglotz vector field on the unit ball of C^n of the form H(z,t)=(a_1 z_1,dots,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.File in questo prodotto:
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