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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
Abstract

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

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