Abstract

A convex subset D of EdE^d is an ellipsoid if all the sections given by hyperplanes are elliptic. We study whether we can restrict the hyperplanes to those that contain one of two fixed linear varieties. In a previous paper in this journal we considered the case where one of the varieties cuts the interior of D, and now we assume that the varieties support D.

Author information

Contact details are reproduced from the original publication and may be historical.

Javier Alonso

Dept. of Mathematics, University of Extremadura, 06071 Badajoz, Spain

jalonso@unex.es

Pedro Martín

Dept. of Mathematics, University of Extremadura, 06071 Badajoz, Spain

pjimenez@unex.es

Keywords

  • Convex body
  • elliptic section
  • ellipsoid

Mathematics Subject Classification

52A20, 46C15

References

  1. J. Alonso, P. Martín: Some characterizations of ellipsoids by sections, Discrete Comput. Geom. 31(4) (2004) 643–654.https://doi.org/10.1007/s00454-004-0803-5Google Scholar
  2. J. Alonso, P. Martín: Convex bodies with sheafs of elliptic sections, J. Convex Analysis 13 (2006) 169–175.https://doi.org/10.68381/jca13011Google Scholar
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Suggested citation

J. Alonso, P. Martín. “Convex Bodies with Sheafs of Elliptic Sections II.” Journal of Convex Analysis 14 (2007), No. 1, 1–11. https://doi.org/10.68381/jca14001

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Published by Heldermann Verlag, 2007. Rights now held by Banach Press LLC.