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Creators/Authors contains: "Rohde, Steffen"

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  1. ; ; ; (, Revista Matemática Iberoamericana)
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  2. ; (, International Mathematics Research Notices)
    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. 
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