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Volume Ratios and a Reverse Isoperimetric Inequality
Author(s) -
Ball Keith
Publication year - 1991
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-44.2.351
Subject(s) - isoperimetric inequality , convex body , mathematics , tetrahedron , combinatorics , volume (thermodynamics) , linear subspace , regular polygon , affine transformation , convex hull , geometry , physics , quantum mechanics
It is shown that if C is an n ‐dimensional convex body then there is an affine image C ˜ of C for which |∂ C ˜ |/| C ˜ (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 ∈[1,∞]),l p nhas maximal volume ratio.