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Hausdorff dimension of the set of extreme points of a self-similar set

Andrew Tetenov·Ivan Davydkin
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Abstract

If the system S of contracting similitudes on $ R^2$ satisfies open convex set condition, then the set F of extreme points of the convex hull $\tilde{K}$ of it's invariant self-similar set K has Hausdorff dimension 0 . If, additionally, all the rotation angles of the similitudes are commensurable with $π$, then the set F is finite and the convex hull $\tilde{K}$ is a convex polygon.

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Andrew Tetenov, Ivan Davydkin. 2002-02-21. Hausdorff dimension of the set of extreme points of a self-similar set. https://arxiv.org/abs/math/0202215

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