A new affine invariant for polytopes and Schneider’s projection problem
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- by Erwin Lutwak, Deane Yang and Gaoyong Zhang PDF
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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.References
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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
- ORCID: 0000-0002-4655-1428
- Email: yang@magnus.poly.edu
- Gaoyong Zhang
- Affiliation: Department of Mathematics, Polytechnic University, Brooklyn, New York 11201
- Email: gzhang@poly.edu
- Received by editor(s): February 26, 2000
- Published electronically: January 5, 2001
- Additional Notes: Research supported, in part, by NSF Grant DMS–9803261
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 1767-1779
- MSC (1991): Primary 52A40
- DOI: https://doi.org/10.1090/S0002-9947-01-02726-X
- MathSciNet review: 1813595