Bi-Lipschitz homogeneous curves in ℝ² are quasicircles

Bishop, Christopher

doi:10.1090/S0002-9947-01-02755-6

Bi-Lipschitz homogeneous curves in $\mathbb {R}^2$ are quasicircles
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by Christopher J. Bishop PDF

Trans. Amer. Math. Soc. 353 (2001), 2655-2663 Request permission

Abstract:

We show that a bi-Lipschitz homogeneous curve in the plane must satisfy the bounded turning condition, and that this is false in higher dimensions. Combined with results of Herron and Mayer this gives several characterizations of such curves in the plane.

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