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St. Petersburg Mathematical Journal

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Approximation of two-dimensional cross-sections of convex bodies by disks and ellipses

Author: V. V. Makeev
Translated by: B. M. Bekker
Original publication: Algebra i Analiz, tom 16 (2004), nomer 6.
Journal: St. Petersburg Math. J. 16 (2005), 1043-1049
MSC (2000): Primary 52A20, 52A27
Published electronically: November 17, 2005
MathSciNet review: 2117452
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Abstract | References | Similar Articles | Additional Information

Abstract: In connection with the well-known Dvoretsky theorem, the following question arises: How close to a disk or to an ellipse can a two-dimensional cross-section through an interior point $ O$ of a convex body $ K\subset \mathbb{R}^n$ be? In the present paper, the attention is focused on a few (close to prime) dimensions $ n$ for which this problem can be solved exactly. Asymptotically, this problem was solved by the author in 1988.

Another problem treated in the paper concerns inscribing a regular polygon in a circle that belongs to a field of circles smoothly embedded into the fibers of the tautological bundle over the Grassmannian manifold $ G_2(\mathbb{R}^n)$.

References [Enhancements On Off] (What's this?)

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Additional Information

V. V. Makeev
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospekt 28, Staryĭ Peterhof, St. Petersburg 198904, Russia

Received by editor(s): October 10, 2003
Published electronically: November 17, 2005
Additional Notes: The work was supported by SSF (grant no. NSh–1914.2003.1).
Article copyright: © Copyright 2005 American Mathematical Society