The Loewner and Hadamard variations
Oliver Roth and Eric Schippers
Source: Illinois J. Math. Volume 52, Number 4
(2008), 1399-1415.
Abstract
We give an explicit formula relating the infinitesimal generators of the Loewner differential equation and the Hadamard variation. This is applied to establish an extension of the Hadamard variation to the case of arbitrary simply-connected domains and to prove the existence of Loewner chains with arbitrary smooth initial generator starting at an arbitrary univalent function which is sufficiently smooth up to the boundary. As another application of this method, we show that every subordination chain ft is differentiable almost everywhere and satisfies a Loewner equation, without assuming that ft'(0) is continuous.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ijm/1258554369
Zentralblatt MATH identifier: 05660665
Mathematical Reviews number (MathSciNet): MR2595774
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