A counterexample to Valette's conjecture
type: Item
instance of: scholarly article
title: A counterexample to Valette's conjecture
zbMATH Open document ID: 1300.52005
DOI: 10.1134/S0081543811080207
author: D. Kharzeev
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2014-09-10T00:00:00Z
review text: The author constructs a simple 4-dimensional counterexample to the following \textit{Conjecture 1.} Let \( K\) be a self-affine body in \({\mathbb R}^d \), \( d \geq 2 \); then \( K \) is either a polytope or affinely equivalent to a product of a convex body with a polytope of lower positive dimension. Some additional assumptions which make this Conjecture true are formulated as well as \textit{Problem 1.} Is the Conjecture \(1\) true for \( d = 3 \)?
reviewed by: Vladimir Golubyatnikov
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 6342484
zbMATH Keywords: self-affine convex bodies
zbMATH Keywords: self-affine partition
zbMATH Keywords: refinable self-affine partition
MaRDI profile type: Publication
Wikidata QID: Q123114930
cites work: Self-affine convex discs are polygons
cites work: Self-affine convex polygons
cites work: Self-affine polytopes. Applications to functional equations and matrix theory
description: scientific article; zbMATH DE number 6342484