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Journal of the London Mathematical Society 1991 s2-44(2):351-359; doi:10.1112/jlms/s2-44.2.351
© 1991 by London Mathematical Society
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© Oxford University Press

Volume Ratios and a Reverse Isoperimetric Inequality

Keith Ball

Trinity College Cambridge CB2 1TQ
Texas A & M University College Station, Texas, USA

It is shown that if C is an n-dimensional convex body then there is an affine image Formula of C for which |{partial}Formula|/|Formula(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 Lp (for eachpisin[1,{infty}]), Formula has maximal volume ratio.


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