Volume ratios and a reverse isoperimetric inequality

Abstract

It is shown that if $C$ is an $n$-dimensional convex body then there is an affine image $\tilde{C}$ of $C$ for which $$\frac{|\partial \tilde{C}|}{|\tilde{C}{|}^{\frac{n-1}{n}}}$$ is no larger than the corresponding expression for a regular $n$-dimensional ``tetrahedron''. It is also shown that among $n$-dimensional subspaces of $L_p$ (for each $p\in [1,\infty ]),{\ell }_p^n$ has maximal volume ratio.\vskip3in

Cited by in corpus (1)

• The quotient girth of normed spaces, and an extension of Schäffer's dual girth conjecture to Grassmannians