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| Title: | The visible part of plane self-similar sets |
| Authors: | Falconer, Kenneth John
Fraser, Jonathan Macdonald |
| Keywords: | Metric Geometry
QA Mathematics |
| Issue Date: | 2013 |
| Citation: | 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 . |
| 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. |
| Version: | Publisher PDF |
| Description: | JMF was supported by an EPSRC grant whilst undertaking this work. |
| Status: | Peer reviewed |
| URI: | http://hdl.handle.net/10023/2756 |
| DOI: | http://dx.doi.org/10.1090/S0002-9939-2012-11312-7 |
| ISSN: | 0002-9939 |
| Type: | Journal article |
| Rights: | © Copyright 2012 American Mathematical Society. First published in Proceedings of the American Mathematical Society 2012, published by the American Mathematical Society) |
| Appears in Collections: | University of St Andrews Research
Pure Mathematics Research
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