# Kostiantyn D. Drach

Phd in mathematics

Link on external publications: arXiv.

## List of selected publications

**K. Drach**
*Some sharp estimates for convex hypersurfaces of pinched normal curvature* //
Journal of Mathematical Physics, Analysis, Geometry,
vol. 11, No. 2, pp. 111-122, 2015

Keywords: convex hypersurface, spaces of constant curvature, pinched normal curvature, $\lambda$-convexity, spherical shell

**A.A. Borisenko, K.D. Drach**
*Comparison theorem for support functions of hypersurfaces* //
Reports of the National Academy of Sciences of Ukraine,
(3): 11-16, 2015

Keywords: comparison theorems, normal curvature, Blaschke's Rolling Theorem, Riemannian support function, polar map

**K. Drach**
*About an isoperimetric property of $\lambda$-convex lunes on the Lobachevsky plane* //
Reports of the National Academy of Sciences of Ukraine,
(11): 11-15, 2014

Keywords: $\lambda$-convex curves, reverse isoperimetric inequality, Pontryagin's Maximum Principle

**A.A. Borisenko, K.D. Drach**
*Isoperimetric Inequality for Curves with Curvature Bounded Below* //
Mathematical Notes,
Vol. 95, No. 5, pp. 14–22., 2014

Keywords: isoperimetric inequality, embedded closed curve, minimal area

**A.A. Borisenko, K.D. Drach**
*Extreme properties of curves with bounded curvature on a sphere* //
Journal of Dynamical and Control Systems,
(DOI) 10.1007/s10883-014-9221-z, 2014

Keywords: $\lambda$-convex curves \and reverse isoperimetric inequality \and Pontryagin's Maximum Principle

**A.A. Borisenko, K.D. Drach**
*Closeness to spheres of hypersurfaces with normal curvature bounded below* //
Sbornik: Mathematics,
204 (11): 1565-1583, 2013

Keywords: Riemannian manifold, sectional curvature, normal curvature of a hypersurface, comparison theorems, $\lambda$-convex hypersurface

**A.A. Borisenko, K.D. Drach**
*About an angle comparison theorem for closed curves* //
Reports of NAS of Ukraine,
(6): 7-11, 2011

**K. Drach**
*Bolyai-Gerwien theorem for unbounded polygons* //
Preprint,
2015

**K. Drach, M. Mixer**
*Minimal covers of equivelar toroidal maps* //
Ars Mathematica Contemporanea,
9:2, 77-91, 2015

Keywords: Minimal covers, Regular and rotary maps, Gaussian and Eisenstein integers

**K. Drach, Yu. Eremenko, A. Krymova**
*Uniquely constructed figures on the sphere* //
Preprint (ukr),
2014