4 papers · 1 filter
A reverse isoperimetric inequality in three-dimensional space forms
Kostiantyn Drach, Gil Solanes, Kateryna Tatarko
A -convex body in a three-dimensional space form of constant curvature is a compact convex set whose boundary has normal curvatures bounded below b…
Stability of reverse isoperimetric inequalities in the plane: area, Cheeger, and inradius
Kostiantyn Drach, Kateryna Tatarko
In this paper, we present sharp stability results for various reverse isoperimetric problems in . Specifically, we prove the stability of the reverse isoperimetric ine…
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…