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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Volume 275, Pages 181–187
(Mi tm3338)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/tm3338 https://www.mathnet.ru/eng/tm/v275/p181
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Abstract page: | 148 | Full-text PDF : | 52 | References: | 48 |
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