Zonoids whose polars are zonoids
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- by Rolf Schneider PDF
- Proc. Amer. Math. Soc. 50 (1975), 365-368 Request permission
Abstract:
It is shown that Euclidean $n$-space contains nonellipsoidal, centrally symmetric convex bodies which, as well as their polars, are zonoids (i.e., can be approximated by finite sums of segments). This disproves a conjecture of E. D. Bolker.References
- Ethan D. Bolker, A class of convex bodies, Trans. Amer. Math. Soc. 145 (1969), 323–345. MR 256265, DOI 10.1090/S0002-9947-1969-0256265-X
- E. D. Bolker, Research Problems: The Zonoid Problem, Amer. Math. Monthly 78 (1971), no. 5, 529–531. MR 1536334, DOI 10.2307/2317764
- Claus Müller, Spherical harmonics, Lecture Notes in Mathematics, vol. 17, Springer-Verlag, Berlin-New York, 1966. MR 0199449
- Rolf Schneider, Zur einem Problem von Shephard über die Projektionen konvexer Körper, Math. Z. 101 (1967), 71–82 (German). MR 218976, DOI 10.1007/BF01135693
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 50 (1975), 365-368
- MSC: Primary 52A20
- DOI: https://doi.org/10.1090/S0002-9939-1975-0470857-2
- MathSciNet review: 0470857