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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Volume 275, Pages 301–303 (Mi tm3345)  
This article is cited in 2 scientific papers (total in 2 papers)

A counterexample to Valette's conjecture

A. Voynov

Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
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Abstract: We disprove a well-known conjecture of D. Vallete (1978), which states that every $d$-dimensional self-affine convex body is a direct product of a polytope with a convex body of lower dimension. It is shown that there are counterexamples for dimension $d=4$. Additional assumptions under which the conjecture is true are discussed.
Received in June 2011
English version:
Proceedings of the Steklov Institute of Mathematics, 2011, Volume 275, Pages 290–292
DOI: https://doi.org/10.1134/S0081543811080207
Bibliographic databases:
Document Type: Article
UDC: 514.174.5+514.172.45
Language: English
Citation: A. Voynov, “A counterexample to Valette's conjecture”, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Collected papers. In commemoration of the 120th anniversary of Boris Nikolaevich Delone's birth, Trudy Mat. Inst. Steklova, 275, MAIK Nauka/Interperiodica, Moscow, 2011, 301–303; Proc. Steklov Inst. Math., 275 (2011), 290–292
Citation in format AMSBIB
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\by A.~Voynov
\paper A counterexample to Valette's conjecture
\inbook Classical and modern mathematics in the wake of Boris Nikolaevich Delone
\bookinfo Collected papers. In commemoration of the 120th anniversary of Boris Nikolaevich Delone's birth
\serial Trudy Mat. Inst. Steklova
\yr 2011
\vol 275
\pages 301--303
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\jour Proc. Steklov Inst. Math.
\yr 2011
\vol 275
\pages 290--292
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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