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Ellipsoids of maximal volume in convex bodies

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Abstract

The largest discs contained in a regular tetrahedron lie in its faces. The proof is closely related to the theorem of Fritz John characterizing ellipsoids of maximal volume contained in convex bodies.

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References

  1. John, F., ‘Extremum problems with inequalities as subsidiary conditions’, Courant Anniversary Volume, Interscience, New York, 1948, pp. 187–204.

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  2. Pełczynski, A., ‘Remarks on John's theorem on the ellipsoid of maximal volume inscribed into a convex body in #x211D;, Nota di Matematicae, volume devoted to the memory of G. Köthe, to appear.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, 77843, College Station, TX, U.S.A.

    Keith Ball

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  1. Keith Ball
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Ball, K. Ellipsoids of maximal volume in convex bodies. Geom Dedicata 41, 241–250 (1992). https://doi.org/10.1007/BF00182424

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  • DOI: https://doi.org/10.1007/BF00182424

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