The multiple-slit version of Loewner's differential equation and pointwise Hölder continuity of driving functions

Abstract

We consider the chordal Loewner differential equation for multiple slits in the upper half-plane and relations between the pointwise Hölder continuity of the driving functions and the generated hulls. The first result generalizes a result of Lind that gives a sufficient condition for driving functions to generate simple curves. The second result translates the property that the hulls locally look like straight lines at their starting points into a condition for the driving functions.

arXiv commentThis paper has been withdrawn by the author. Errors in Theorem 1.2 and Theorem 1.3. See arXiv:1501.04507 (Chapter 3) for the corrected statements

Cited by in corpus (1)

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