A new affine invariant for polytopes and Schneider’s projection problem

Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong

doi:10.1090/S0002-9947-01-02726-X

A new affine invariant for polytopes and Schneider’s projection problem
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by Erwin Lutwak, Deane Yang and Gaoyong Zhang PDF

Trans. Amer. Math. Soc. 353 (2001), 1767-1779 Request permission

Abstract:

New affine invariant functionals for convex polytopes are introduced. Some sharp affine isoperimetric inequalities are established for the new functionals. These new inequalities lead to fairly strong volume estimates for projection bodies. Two of the new affine isoperimetric inequalities are extensions of Ball’s reverse isoperimetric inequalities.

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