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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Volume 275, Pages 181–187 (Mi tm3338)  
This article is cited in 1 scientific paper (total in 1 paper)

The illumination conjecture for spindle convex bodies

Károly Bezdekabc

a Department of Mathematics, University of Pannonia, Veszprém, Hungary
b Institute of Mathematics, Eötvös Loránd University, Budapest, Hungary
c Department of Mathematics and Statistics, University of Calgary, Canada
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Abstract: A subset of the d-dimensional Euclidean space having nonempty interior is called a spindle convex body if it is the intersection of (finitely or infinitely many) congruent d-dimensional closed balls. A spindle convex body is called a “fat” one if it contains the centers of its generating balls. The main result of this paper is a proof of the illumination conjecture for “fat” spindle convex bodies in dimensions greater than or equal to 15.
Received in April 2011
English version:
Proceedings of the Steklov Institute of Mathematics, 2011, Volume 275, Pages 169–176
DOI: https://doi.org/10.1134/S0081543811080116
Bibliographic databases:
Document Type: Article
UDC: 514.17
Language: English
Citation: Károly Bezdek, “The illumination conjecture for spindle convex bodies”, 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, 181–187; Proc. Steklov Inst. Math., 275 (2011), 169–176
Citation in format AMSBIB
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\paper The illumination conjecture for spindle convex bodies
\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
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\vol 275
\pages 181--187
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • https://www.mathnet.ru/eng/tm/v275/p181
    • This publication is cited in the following 1 articles:
    1. Károly Bezdek, Ilya Ivanov, Cameron Strachan, “Illuminating spiky balls and cap bodies”, Discrete Mathematics, 346:1 (2023), 113135  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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