85 citations · 140 across the 13 of their papers we have counts for
7 papers · 1 filter
Chebyshev constants for the unit circle
Gergely Ambrus, Keith M. Ball, T. Erdélyi
It is proven that for any system of n points z_1, ..., z_n on the (complex) unit circle, there exists another point z of norm 1, such that Equality…
Stability of some versions of the Prékopa-Leindler inequality
Károly J. Böröczky, Keith M. Ball
Two consequences of the stability version of the one dimensional Prékopa-Leindler inequality are presented. One is the stability version of the Blaschke-Santaló inequality, and the…
The plank problem for symmetric bodies
Keith Ball
Given a symmetric convex body and hyperplanes in an Euclidean space, there is a translate of a multiple of , at least times as large, inside , whose in…
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…
Volume ratios and a reverse isoperimetric inequality
Keith Ball
It is shown that if is an -dimensional convex body then there is an affine image of for which $${|\partial \widetilde C|\over |\widetilde C|^{n-1\over n}}…
Shadows of convex bodies
Keith Ball
It is proved that if is a convex body in then has an affine image (of non-zero volume) so that if is any 1-codimensional orthogonal projecti…