Title: Chordal generators and the hydrodynamic normalization for the unit ball
Abstract:Let c 0 and denote by K.;ވ c/ the set of all infinitesimal generators G W ވ !ރ on the upper half-plane ވ such that lim sup y!1 y jG.iy /j Ä c.This class is related to univalent functions f W ...Let c 0 and denote by K.;ވ c/ the set of all infinitesimal generators G W ވ !ރ on the upper half-plane ވ such that lim sup y!1 y jG.iy /j Ä c.This class is related to univalent functions f W ވ !ވ with hydrodynamic normalization and appears in the so-called chordal Loewner equation.In this paper, we generalize the class K.;ވ c/ and the hydrodynamic normalization to the Euclidean unit ball in ރ n .The generalization is based on the observation that G 2 K.;ވ c/ can be characterized by an inequality for the hyperbolic length of G.z/. 1. Introduction 203 2. Chordal generators in higher dimensions 207 3. Slices 209 4. Univalent functions with hydrodynamic normalization 213 Appendix: Proof of Lemma 3.2Read More