The visible part of plane self-similar sets
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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.
Falconer , K J & Fraser , J M 2013 , ' The visible part of plane self-similar sets ' Proceedings of the American Mathematical Society , vol 141 , no. 1 , pp. 269-278 . DOI: 10.1090/S0002-9939-2012-11312-7
Proceedings of the American Mathematical Society
© Copyright 2012 American Mathematical Society. First published in Proceedings of the American Mathematical Society 2012, published by the American Mathematical Society)
JMF was supported by an EPSRC grant whilst undertaking this work.
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