The visible part of plane self-similar sets

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12 Citations (Scopus)

Abstract

Given a compact subset F of R2, the visible part VθF of F from direction θ is
the set of x in F such that the half-line from x in direction θ intersects F only at
x. It is suggested that if dimH F ≥ 1 then dimH VθF = 1 for almost all θ , where
dimH denotes Hausdorff dimension. We conrm this when F is a self-similar set
satisfying the convex open set condition and such that the orthogonal projection
of F onto every line is an interval. In particular the underlying similarities may
involve arbitrary rotations and F need not be connected.

Original languageEnglish
Pages (from-to)269-278
JournalProceedings of the American Mathematical Society
Volume141
Issue number1
Early online date16 May 2012
DOIs
Publication statusPublished - 2013

Keywords

  • Metric Geometry

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