A Schwarz lemma on complex ellipsoids
We give a Schwarz lemma on complex ellipsoids.
A characterization of linear automorphisms of the Euclidean ball
Let B be the open unit ball for a norm on . Let f:B → B be a holomorphic map with f(0) = 0. We consider a condition implying that f is linear on . Moreover, in the case of the Euclidean ball , we show that f is a linear automorphism of under this condition.
k-convexity in several complex variables
We define and investigate the notion of k-convexity in the sense of Mejia-Minda for domains in ℂⁿ and also that of k-convex mappings on the Euclidean unit ball.
Loewner chains and quasiconformal extension of holomorphic mappings
Let f(z,t) be a Loewner chain on the Euclidean unit ball B in ℂⁿ. Assume that f(z) = f(z,0) is quasiconformal. We give a sufficient condition for f to extend to a quasiconformal homeomorphism of onto itself.
Spirallike mappings and univalent subordination chains in
In this paper we consider non-normalized univalent subordination chains and the connection with the Loewner differential equation on the unit ball in . To this end, we study the most general form of the initial value problem for the transition mapping, and prove the existence and uniqueness of solutions. Also we introduce the notion of generalized spirallikeness with respect to a measurable matrix-valued mapping, and investigate this notion from the point of view of non-normalized univalent subordination...
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