Resonances in Loewner equations |
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| Authors: | Leandro Arosio |
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| Institution: | Dipartimento di Matematica, Università di Roma “La Sapienza”, Piazzale A. Moro 5, 00185 Roma, Italy |
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| Abstract: | We prove that given a Herglotz vector field on the unit ball of Cn of the form H(z,t)=(a1z1,…,anzn)+O(2|z|) with  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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| Keywords: | Loewner chains in several variables Loewner equations Evolution families Resonances |
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