Basins of attraction in Loewner equations

Details Basins of attraction in Loewner equations Basins of attraction in Loewner equations

2011-08-30

arxiv.org/abs/1108.6000v2

Mathematics

Complex Variables

9 pages, revised exposition, improved results, added references

Scientific paper

We prove that any Loewner PDE whose driving term h(z,t) vanishes at the origin, and satisfies the bunching condition r m(Dh(0,t))\geq k(Dh(0,t)) for some r\in R^+, admits a solution given by univalent mappings (f_t: B^q\to C^q). This is done by discretizing time and considering the abstract basin of attraction. If r<2, then the union of the images f_t(\B^q) of a such solution is biholomorphic to C^q.

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