Loewner equations on complete hyperbolic domains

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• 作者：Leandro Arosio¹ ; ^{arosio@altamatematica.it} ; ^{leandroarosio@gmail.com}
• 关键词：Loewner chains in several variables ; Loewner equations ; Evolution families ; Resonances
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2013
• 出版时间：15 February, 2013
• 年：2013
• 卷：398
• 期：2
• 页码：609-621
• 全文大小：278 K

文摘

We prove that, on a complete hyperbolic domain , any Loewner PDE associated with a Herglotz vector field of the form , where the eigenvalues of have strictly negative real part, admits a solution given by a family of univalent mappings which satisfies . If no real resonance occurs among the eigenvalues of , then the family is uniformly bounded in a neighborhood of the origin. We also give a generalization of Pommerenke¡¯s univalence criterion on complete hyperbolic domains.