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Title: The Loewner Energy of Loops and Regularity of Driving Functions
Abstract Loewner driving functions encode simple curves in 2D simply connected domains by real-valued functions. We prove that the Loewner driving function of a $C^{1,\beta }$ curve (differentiable parametrization with $\beta$-Hölder continuous derivative) is in the class $C^{1,\beta -1/2}$ if $1/2<\beta \leq 1$, and in the class $C^{0,\beta + 1/2}$ if $0 \leq \beta \leq 1/2$. This is the converse of a result of Carto Wong [26] and is optimal. We also introduce the Loewner energy of a rooted planar loop and use our regularity result to show the independence of this energy from the basepoint.  more » « less
Award ID(s):
1700069
PAR ID:
10177850
Author(s) / Creator(s):
;
Date Published:
Journal Name:
International Mathematics Research Notices
ISSN:
1073-7928
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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