Eugeny A. Olin

Eugeny A. Olin

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11
Publications
339
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14
Citations

Publications

Publications (11)
Article
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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
Article
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 curvatures are different at infinity in Funk geometry.
Article
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T -кривизной. Доказывается, что при определенных ограничениях на нормальную кривизну такие гиперповерхности являются выпуклыми, вложенными, гомеоморфными сфере. Для этого доказывается обобщение теоремы Рауха для экспоненциального отображения относительно гиперповерхности и показывается выпуклость параллельных гиперповерхностей.
Article
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. 2000 Mathematics Subject Classification 53C60. Let M be a complete Finsler manifold. Then 1. A set A is s...
Article
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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 v...
Article
Full-text available
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 metric ball to the area of the metric sphere in Hilbert geometry. Derived estimates agree with the well-known fact in the Lobachevsky space
Article
Full-text available
Locally convex compact immersed hypersurfaces in the Finsler—Hadamard space with bounded T-curvature are considered. Under certain conditions on normal curvatures, such hypersurfaces are proved to be convex, embedded, and homeomorphic to the sphere. To this end, the Rauch theorem is generalized to exponential maps of hypersurfaces and the convexity...

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