Curvatures of spheres in Hilbert geometry
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
math.DG↗
arXiv subjects
Alexandr A. Borisenko
Publications and source records attributed to Alexandr A. Borisenko.
Global Structure of Locally Convex Hypersurfaces in Finsler-Hadamard Manifolds
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 of convex body under certain conditions on the normal curvatures
math.DG↗
Some comparison theorems in Finsler-Hadamard manifolds
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 estimates to find the limit at the infinity for this ratio. Derived estimates are the generalization of the well-known result in Riemannian geometry. We also estimate the volume growth entropy for the balls in such manifolds.
math.DG↗