Research@StAndrews
 
The University of St Andrews

Research@StAndrews:FullText >
University of St Andrews Research >
University of St Andrews Research >
University of St Andrews Research >

Please use this identifier to cite or link to this item: http://hdl.handle.net/10023/2756
This item has been viewed 4 times in the last year. View Statistics

Files in This Item:

File Description SizeFormat
FalconerProcAmMathSoc2012VisiblePart.pdf505.69 kBAdobe PDFView/Open
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



This item is protected by original copyright

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

 

DSpace Software Copyright © 2002-2012  Duraspace - Feedback
For help contact: Digital-Repository@st-andrews.ac.uk | Copyright for this page belongs to St Andrews University Library | Terms and Conditions (Cookies)