K. Ball

activity

19922026

most citedThe plank problem for symmetric bodies

85 citations · 140 across the 13 of their papers we have counts for

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Showing 1992Show all

5 papers · 1 filter

math.MG1992★ 85 cited

The plank problem for symmetric bodies

Keith Ball

Given a symmetric convex body $C$ and $n$ hyperplanes in an Euclidean space, there is a translate of a multiple of $C$ , at least $\frac{1}{n + 1}$ times as large, inside $C$ , whose in…

math.MG1992

Ellipsoids of maximal volume in convex bodies

Keith Ball

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

math.MG1992★ 1 cited

Volume ratios and a reverse isoperimetric inequality

Keith Ball

It is shown that if $C$ is an $n$ -dimensional convex body then there is an affine image $C$ of $C$ for which $${|\partial \widetilde C|\over |\widetilde C|^{n-1\over n}}…

math.MG1992

Shadows of convex bodies

Keith Ball

It is proved that if $C$ is a convex body in $R^{n}$ then $C$ has an affine image $C$ (of non-zero volume) so that if $P$ is any 1-codimensional orthogonal projecti…

math.MG1992

Convex bodies with few faces

Keith Ball, Alain Pajor

It is proved that if $u_{1}, \dots, u_{n}$ are vectors in $R^{k}, k \leq n, 1 \leq p < \infty$ and $r = (\frac{1}{k} 1 \sum n ∣ u_{i} ∣^{p})^{\frac{1}{p}}$ then the volume of the symmetric…