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Transactions of the American Mathematical Society

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


Authors: Erwin Lutwak, Deane Yang and Gaoyong Zhang
Journal: Trans. Amer. Math. Soc. 353 (2001), 1767-1779
MSC (1991): Primary 52A40
DOI: https://doi.org/10.1090/S0002-9947-01-02726-X
Published electronically: January 5, 2001
MathSciNet review: 1813595
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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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Additional Information

Erwin Lutwak
Affiliation: Department of Mathematics, Polytechnic University, Brooklyn, New York 11201
Email: elutwak@poly.edu

Deane Yang
Affiliation: Department of Mathematics, Polytechnic University, Brooklyn, New York 11201
Email: yang@magnus.poly.edu

Gaoyong Zhang
Affiliation: Department of Mathematics, Polytechnic University, Brooklyn, New York 11201
Email: gzhang@poly.edu

DOI: https://doi.org/10.1090/S0002-9947-01-02726-X
Keywords: Affine isoperimetric inequalities, reverse isoperimetric inequalities, projection bodies, asymptotic inequalities
Received by editor(s): February 26, 2000
Published electronically: January 5, 2001
Additional Notes: Research supported, in part, by NSF Grant DMS–9803261
Article copyright: © Copyright 2001 American Mathematical Society

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