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

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

2012-02-17

arxiv.org/abs/1202.3948v1

Ann. Acad. Sci. Fenn. Math. 37 (2012), 191-201

Mathematics

Complex Variables

13 pages

Scientific paper

10.5186/aasfm.2012.3720

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.

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