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Phase transition for a family of complex-driven Loewner hulls

Joan Lind and Jeffrey Utley

Vol. 15 (2022), No. 3, 447–474

Building on H. Tran’s study of Loewner hulls generated by complex-valued driving functions, which showed the existence of a phase transition, we answer the question of whether the phase transition for complex-driven hulls matches the phase transition for real-driven hulls. This is accomplished through a detailed study of the Loewner hulls generated by driving functions c1 t and cτ + t for c and τ 0. This family also provides examples of new geometric behavior that is possible for complex-driven hulls but prohibited for real-driven hulls.

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Loewner evolution, Loewner hulls
Mathematical Subject Classification
Primary: 30C35
Received: 29 June 2021
Revised: 8 November 2021
Accepted: 8 November 2021
Published: 2 December 2022

Communicated by Michael Dorff
Joan Lind
Department of Mathematics
University of Tennessee
Knoxville, TN
United States
Jeffrey Utley
Department of Mathematics
University of Tennessee
Knoxville, TN
United States