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math.DG2026
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…
math.DG2026
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…
math.DG2025
The Blaschke rolling theorem in Riemannian manifolds of bounded curvature
Kostiantyn Drach
We generalize the classical Blaschke Rolling Theorem to convex domains in Riemannian manifolds of bounded sectional curvature and arbitrary dimension. Our results are sharp and, in…