1 citations · 1 across the 2 of their papers we have counts for
5 papers
On different curvatures of spheres in Funk geometry
Eugeny A. Olin
We compute the series expansions for the normal curvatures of hyperspheres, the Finsler and Rund curvatures of circles in Funk geometry as the radii tend to infinity. These three c…
Curvatures of spheres in Hilbert geometry
Alexandr A. Borisenko, Eugeny A. Olin
We prove that the normal curvatures of hyperspheres, the Rund curvature, and the Finsler curvature of circles in Hilbert geometry tend to 1 as the radii tend to infinity
Some comparison theorems in Finsler-Hadamard manifolds
Alexandr A. Borisenko, Eugeny A. Olin
We give upper and lower bounds for the ratio of the volume of metric ball to the area of the metric sphere in Finsler-Hadamard manifolds with pinched S-curvature. We apply these es…
Asymptotic Properties of Hilbert Geometry
Alexander A. Borisenko, Eugeny A. Olin
We show that the spheres in Hilbert geometry have the same volume growth entropy as those in the Lobachevsky space. We give the asymptotic estimates for the ratio of the volume of…
Global Structure of Locally Convex Hypersurfaces in Finsler-Hadamard Manifolds
Alexandr A. Borisenko, Eugeny A. Olin
Locally convex compact immersed hypersurfaces in Finsler-Hadamard manifolds with bounded T-curvature are considered. We prove that such hypersurfaces are embedded as the boundary o…