Weak Quasicircles Have Lipschitz Dimension 1
David M. Freeman
TL;DR
This paper proves that the Lipschitz dimension of weak quasicircles and arcs, including bounded turning Jordan circles, is always equal to 1, establishing a fundamental geometric property.
Contribution
It establishes that all weak quasicircles and arcs have Lipschitz dimension exactly 1, extending previous results to a broader class of geometric objects.
Findings
Lipschitz dimension of bounded turning Jordan circles is 1
Lipschitz dimension of weak quasicircles is 1
Lipschitz dimension of arcs is 1
Abstract
We prove that the Lipschitz dimension of any bounded turning Jordan circle or arc is equal to 1. In particular, the Lipschitz dimension of any weak quasicircle or arc is equal to 1.
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Taxonomy
TopicsAnalytic and geometric function theory · Geometric Analysis and Curvature Flows · Geometric and Algebraic Topology