4 papers
Curvature functionals on convex bodies
Kateryna Tatarko, Elisabeth M. Werner
We investigate the weighted affine surface areas which appear in the recently established Steiner formula of the Brunn Minkowski theory. We show that they are val…
Unique determination of ellipsoids by their dual volumes and the moment problem
Sergii Myroshnychenko, Kateryna Tatarko, Vladyslav Yaskin
Gusakova and Zaporozhets conjectured that ellipsoids in are uniquely determined (up to an isometry) by their Steiner polynomials. Petrov and Tarasov confirmed this co…
A Steiner formula in the Brunn Minkowski theory
Kateryna Tatarko, Elisabeth M. Werner
We prove an analogue of the classical Steiner formula for the affine surface area of a Minkowski outer parallel body for any real parameters . We show that the classical S…
A sausage body is a unique solution for a reverse isoperimetric problem
Roman Chernov, Kostiantyn Drach, Kateryna Tatarko
We consider the class of -concave bodies in ; that is, convex bodies with the property that each of their boundary points supports a tangent ball of radius $1/λ…