A sharp exceptional set estimate for visibility

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http://hdl.handle.net/10138/232900

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Orponen , T 2018 , ' A sharp exceptional set estimate for visibility ' , Bulletin of the London Mathematical Society , vol. 50 , no. 1 , pp. 1-6 . https://doi.org/10.1112/blms.12103

Title: A sharp exceptional set estimate for visibility
Author: Orponen, Tuomas
Other contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2018-02
Language: eng
Number of pages: 6
Belongs to series: Bulletin of the London Mathematical Society
ISSN: 0024-6093
DOI: https://doi.org/10.1112/blms.12103
URI: http://hdl.handle.net/10138/232900
Abstract: A Borel set B<subset of>Rn is visible from xRn, if the radial projection of B with base point x has positive Hn-1 measure. I prove that if dimB>n-1, then B is visible from every point xRn\E, where E is an exceptional set with dimension dimE2(n-1)-dimB. This is the sharp bound for all n2. Many parts of the proof were already contained in a recent previous paper by P. Mattila and the author, where a weaker bound for dimE was derived as a corollary from a certain slicing theorem. Here, no improvement to the slicing result is obtained; in brief, the main observation of the present paper is that the proof method gives the optimal result, when applied directly to the visibility problem.
Subject: 28A75
HAUSDORFF DIMENSION
PROJECTIONS
111 Mathematics
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