34 citations · 125 across the 47 of their papers we have counts for
5 papers · 1 filter
Polynomial valuations on plane polygons
Askold Khovanskii, Valentina Kiritchenko, Vladlen Timorin
Scissors congruence problems involving translations have prompted the study of translation invariant simple valuations. We review this classical theory from a naive and consistent…
On the theory of coconvex bodies
Askold Khovanskii, Vladlen Timorin
If the complement of a closed convex set in a closed convex cone is bounded, then this complement minus the apex of the cone is called a coconvex set. Coconvex sets appear in singu…
Aleksandrov-Fenchel inequality for coconvex bodies
Askold Khovanskii, Vladlen Timorin
We prove a version of the Aleksandrov-Fenchel inequality for mixed volumes of coconvex bodies. This version is motivated by an inequality from commutative algebra relating intersec…
Circles and Quadratic Maps Between Spheres
Vladlen Timorin
Consider an analytic map of a neighborhood of 0 in a vector space to a Euclidean space. Suppose that this map takes all germs of lines passing through 0 to germs of circles. Such a…
Circles and Clifford Algebras
Vladlen Timorin
Consider a smooth map from a neighborhood of the origin in a real vector space to a neighborhood of the origin in a Euclidean space. Suppose that this map takes all germs of lines…