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A stability result for a volume ratio

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Abstract

For a convex body K in ℝn, the volume quotient is the ratio of the smallest volume of the circumscribed ellipsoids to the largest volume of the inscribed ellipsoids, raised to power 1/n. It attains its maximum if and only if K is a simplex. We improve this result by estimating the Banach-Mazur distance of K from a simplex if the volume quotient of K is close to the maximum.

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References

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Authors and Affiliations

  1. Mathematisches Institut, Albert-Ludwigs-Universität, Eckerstr. 1, D-79104, Freiburg. i. Br., Germany

    Daniel Hug & Rolf Schneider

Authors
  1. Daniel Hug
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  2. Rolf Schneider
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Corresponding author

Correspondence to Daniel Hug.

Additional information

This work was supported in part by the European Network PHD, FP6 Marie Curie Actions, RTN, Contract MCRN-511953.

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Hug, D., Schneider, R. A stability result for a volume ratio. Isr. J. Math. 161, 209–219 (2007). https://doi.org/10.1007/s11856-007-0079-6

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  • DOI: https://doi.org/10.1007/s11856-007-0079-6

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