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A new affine invariant for polytopes and Schneider's projection problem
Author(s):
Erwin
Lutwak;
Deane
Yang;
Gaoyong
Zhang
Journal:
Trans. Amer. Math. Soc.
353
(2001),
1767-1779.
MSC (1991):
Primary 52A40
Posted:
January 5, 2001
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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:
10.1090/S0002-9947-01-02726-X
PII:
S 0002-9947(01)02726-X
Keywords:
Affine isoperimetric inequalities,
reverse isoperimetric inequalities,
projection bodies,
asymptotic inequalities
Received by editor(s):
February 26, 2000
Posted:
January 5, 2001
Additional Notes:
Research supported, in part, by NSF Grant DMS--9803261
Copyright of article:
Copyright
2001,
American Mathematical Society
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