[HTML][HTML] A sausage body is a unique solution for a reverse isoperimetric problem

R Chernov, K Drach, K Tatarko - Advances in Mathematics, 2019 - Elsevier
We consider the class of λ-concave bodies in R n+ 1; that is, convex bodies with the property
that each of their boundary points supports a tangent ball of radius 1/λ that lies locally …

Reverse isoperimetric problems under curvature constraints

K Drach, K Tatarko - arXiv preprint arXiv:2303.02294, 2023 - arxiv.org
In this paper we solve several reverse isoperimetric problems in the class of $\lambda $-
convex bodies, ie, convex bodies whose curvature at each point of their boundary is …

The Blaschke rolling theorem in Riemannian manifolds of bounded curvature

K Drach - arXiv preprint arXiv:2404.02739, 2024 - arxiv.org
arXiv:2404.02739v1 [math.DG] 3 Apr 2024 Page 1 THE BLASCHKE ROLLING THEOREM IN
RIEMANNIAN MANIFOLDS OF BOUNDED CURVATURE KOSTIANTYN DRACH Abstract. We …

Inradius estimates for convex domains in 2-dimensional Alexandrov spaces

K Drach - Analysis and Geometry in Metric Spaces, 2018 - degruyter.com
Inradius Estimates for Convex Domains in 2-Dimensional Alexandrov Spaces Page 1 Open
Access. © 2018 Kostiantyn Drach, published by De Gruyter. This work is licensed under the …

[PDF][PDF] On some problems in Random Matrix Theory and Convex Geometry

K Tatarko - 2020 - era.library.ualberta.ca
This thesis is devoted to several problems in Random Matrix Theory and Convex Geometry.
Its content is based on four papers. In the first part, we establish an upper estimate for the …