The multiple-slit version of Loewner's differential equation and pointwise H\"older 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 H\"older 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.