Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 581-599

THE LOEWNER EQUATION FOR MULTIPLE HULLS

Andrew Starnes

University of Hartford, Mathematics Department
West Hartford, CT 06117, U.S.A.; starnes 'at' hartford.edu

Abstract. Kager, Nienhuis, and Kadanoff conjectured that the hull generated from the Loewner equation driven by two constant functions with constant weights could be generated by a single rapidly and randomly oscillating function. We prove their conjecture and generalize to multiple continuous driving functions. In the process, we generalize to multiple hulls a result of Roth and Schleissinger that says multiple slits can be generated by constant weight functions. The proof gives a simulation method for hulls generated by the multiple Loewner equation.

2010 Mathematics Subject Classification: Primary 30C35.

Key words: Loewner.

Reference to this article: A. Starnes: The Loewner equation for multiple hulls. Ann. Acad. Sci. Fenn. Math. 44 (2019), 581-599.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4435