Fixing and almost fixing a planar convex body
Metric Geometry
2018-12-04 v2
Abstract
A set of points a 1 ,. .. , a n fixes a planar convex body K if the points are on bdK, the boundary of K, and if any small move of K brings some point of the set in intK, the interior of K. The points a 1 ,. .. , a n bdK almost fix K if, for any neighbourhoods V i of a i (i = 1,. .. , n), there are pairs of points a i , a i V i bdK such that a 1 , a 1 ,. .. , a n fix K. This note compares several definitions of these notions and gives first order conditions for a 1 ,. .. , a n bdK to fix, and to almost fix, K.
Cite
@article{arxiv.1708.02745,
title = {Fixing and almost fixing a planar convex body},
author = {Augustin Fruchard},
journal= {arXiv preprint arXiv:1708.02745},
year = {2018}
}