Regularity of Loewner Curves
Abstract
The Loewner equation encrypts a growing simple curve in the plane into a real-valued driving function. We show that if the driving function λ is in Cβ with β>2 (or real analytic) then the Loewner curve is in Cβ + 12 (respectively analytic). This is a converse to a result by Earle and Epstein and extends a result of Wong.
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