vix.ing · top · new · best · stats · spec

Counterexamples Related to Rotations of Shadows of Convex Bodies

2015/05/21 by M. Angeles Alfonseca, Alfonseca, M. Angeles, Michelle Cordier +1
Mathematics · #44A12 #52A20 #52A38 #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:44A12 #msc:52A20 #msc:52A38

paper · pdf · doi:10.48550/arxiv.1505.05817

17 pages, 11 figures

arxiv created 2015/05/21 · arxiv updated 2015/05/22

Abstract

We construct examples of two convex bodies K,L in ℝn, such that every projection of K onto a (n-1)-dimensional subspace can be rotated to be contained in the corresponding projection of L, but K itself cannot be rotated to be contained in L. We also find necessary conditions on K and L to ensure that K can be rotated to be contained in L if all the (n-1)-dimensional projections have this property.

Related