Vlasenko D. Convex hypersurfaces in Riemannian spaces of nonpositive curvature

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0406U000294

Thesis Registration Form

0406U000294.pdf

Applicant for

Specialization

  • 01.01.04 - Геометрія і топологія

04-01-2006

Specialized Academic Board

К64.051.11

Essay

The criterion of embedding for immersed locally convex hypersurface in the Lobachevsky space is obtained. The bounds for the ratio of a volume of a convex body to an area of its boundary in Lobachevsky space and in the Hadamard manifold are obtained. Conditions under which a hypersurface in the Hadamard manifold is isomeric to a metric sphere in the Lobachevsky space. It is show, that h-convex surfaces in the Lobachevsky space are metric spaces of a non-negative curvature in A.D. Aleksandrov's sense.

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