Minkowski valuations and generalized valuations
نویسندگان
چکیده
منابع مشابه
Minkowski Valuations
Centroid and difference bodies define SL(n) equivariant operators on convex bodies and these operators are valuations with respect to Minkowski addition. We derive a classification of SL(n) equivariant Minkowski valuations and give a characterization of these operators. We also derive a classification of SL(n) contravariant Minkowski valuations and of Lp-Minkowski valuations. 2000 AMS subject c...
متن کاملRotation Equivariant Minkowski Valuations
The projection body operator Π, which associates with every convex body in Euclidean space Rn its projection body, is a continuous valuation, it is invariant under translations and equivariant under rotations. It is also well known that Π maps the set of polytopes in Rn into itself. We show that Π is the only non-trivial operator with these properties. MSC 2000: 52B45, 52A20
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A description of continuous rigid motion compatible Minkowski valuations is established. As an application we present a Brunn–Minkowski type inequality for intrinsic volumes of these valuations.
متن کاملMinkowski valuations on lattice polytopes
A complete classification is established of Minkowski valuations on lattice polytopes that intertwine the special linear group over the integers and are translation invariant. In the contravariant case, the only such valuations are multiples of projection bodies. In the equivariant case, the only such valuations are generalized difference bodies combined with multiples of the newly defined disc...
متن کاملMinkowski valuations on convex functions
A classification of [Formula: see text] contravariant Minkowski valuations on convex functions and a characterization of the projection body operator are established. The associated LYZ measure is characterized. In addition, a new [Formula: see text] covariant Minkowski valuation on convex functions is defined and characterized.
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ژورنال
عنوان ژورنال: Journal of the European Mathematical Society
سال: 2018
ISSN: 1435-9855
DOI: 10.4171/jems/801