5 citations · 33 across the 23 of their papers we have counts for
16 papers · 1 filter
Geodesic loops on tetrahedra in spaces of constant sectional curvature
Alexander A. Borisenko, Vicente Miquel
Geodesic loops on polyhedra were studied only for Euclidean space and it was known that there are no simple geodesic loops on regular tetrahedra. Here we prove that: 1) On the sphe…
Inscribed and circumscribed radius of -convex hypersurfaces in Hadamard manifolds
Alexander A. Borisenko, Vicente Miquel
Let be a convex polygon in a Hadamard surface with curvature satisfying . We give an upper bound of the circumradius of in terms of a lower…
A discrete Blaschke Theorem for convex polygons in -dimensional space forms
Alexander Borisenko, Vicente Miquel
Let be a -space form. Let be a convex polygon in . For these polygons, we define (and justify) a curvature at each vertex of the polygon and and prove the…
The estimation of the length of a convex curve in two-dimensional Alexandrov space
Alexander A. Borisenko
It is proved the generalization of Toponogov theorem about the length of the curve in two-dimensional Riemannian manifolds in the case of two-dimensional Alexandrov spaces.
Degenerate Bianchi transformations for three-dimensional pseudo-spherical submanifolds in
A. A. Borisenko, V. O. Gorkavyy
Three-dimensional pseudo-spherical submanifolds in , whose Bianchi transformations are degenerate of rank 2, are studied. A complete description of such submanifolds i…
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…