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math.DG2018
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…
math.DG2018
Inradius estimates for convex domains in 2-dimensional Alexandrov spaces
Kostiantyn Drach
We obtain sharp lower bounds on the radii of inscribed balls for strictly convex isoperimetric domains lying in a 2-dimensional Alexandrov metric space of curvature bounded below.…
math.DG2016
Extreme properties of curves with bounded curvature on a sphere
Alexander Borisenko, Kostiantyn Drach
We give a sharp lower bound on the area of the domain enclosed by an embedded curve lying on a two-dimensional sphere, provided that geodesic curvature of this curve is bounded fro…