AbstractLet Π be the projection operator, which maps every polytope to its projection body. It is well known that Π maps the set of polytopes, Pn, in Rn into Pn, that it is a valuation, and that for every P∈Pn, ΠP is affinely associated to P. It is shown that these properties characterize the projection operator Π. This proves a conjecture by Lutwak
AbstractThe following theorem is discussed. Let X be a compact subset of the unit sphere in Cn whose...
AbstractAbstract valuations on a topological space X are functions that map open sets to 0, 1, or on...
We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere S...
AbstractLet Π be the projection operator, which maps every polytope to its projection body. It is we...
on the occasion of his sixty-fifth birthday The projection body operator Π, which associates with ev...
AbstractLet K⊂Rn be a convex body (a compact, convex subset with non-empty interior), ΠK its project...
AbstractLet F be an ordered field, and let p denote the family of all convex polytopes in the d-dime...
AbstractProjection and intersection bodies define continuous and GL(n) contravariant valuations. The...
Projection and intersection bodies define continuous and GL(n) contravariant valuations. They played...
In geometric valuation theory, well-known examples of Minkowski valuations intertwining the special ...
Lattice polytopes are convex hulls of finitely many points with integer coordinates in ${\mathbb R}^...
AbstractThe set of scaled projections of a vector onto the column space of a matrix has recently bee...
AbstractLet L be a lattice (that is, a Z-module of finite rank), and let L=P(L) denote the family of...
AbstractA polytope P⊆[0,1)d and an α→∈[0,1)d induce a so-called Hartman sequence h(P,α→)∈{0,1}Z whic...
AbstractWe address several basic questions that arise in the use of projection in combinatorial opti...
AbstractThe following theorem is discussed. Let X be a compact subset of the unit sphere in Cn whose...
AbstractAbstract valuations on a topological space X are functions that map open sets to 0, 1, or on...
We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere S...
AbstractLet Π be the projection operator, which maps every polytope to its projection body. It is we...
on the occasion of his sixty-fifth birthday The projection body operator Π, which associates with ev...
AbstractLet K⊂Rn be a convex body (a compact, convex subset with non-empty interior), ΠK its project...
AbstractLet F be an ordered field, and let p denote the family of all convex polytopes in the d-dime...
AbstractProjection and intersection bodies define continuous and GL(n) contravariant valuations. The...
Projection and intersection bodies define continuous and GL(n) contravariant valuations. They played...
In geometric valuation theory, well-known examples of Minkowski valuations intertwining the special ...
Lattice polytopes are convex hulls of finitely many points with integer coordinates in ${\mathbb R}^...
AbstractThe set of scaled projections of a vector onto the column space of a matrix has recently bee...
AbstractLet L be a lattice (that is, a Z-module of finite rank), and let L=P(L) denote the family of...
AbstractA polytope P⊆[0,1)d and an α→∈[0,1)d induce a so-called Hartman sequence h(P,α→)∈{0,1}Z whic...
AbstractWe address several basic questions that arise in the use of projection in combinatorial opti...
AbstractThe following theorem is discussed. Let X be a compact subset of the unit sphere in Cn whose...
AbstractAbstract valuations on a topological space X are functions that map open sets to 0, 1, or on...
We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere S...
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