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- W2083379421 abstract "ABsTRAcr. Let T be a compact convex region in an n-dimensional Riemannian space, ks be the minimum sectional curvature in T, and K > 0 be the minimum normal curvature of the boundary of T. Denote by PI() a P-dimensional sphere, plane or hyperbolic plane of curvature t. We assume that kI, K are such that on P2(k3) there exists a circumference of curvature K. Let Ro = RO(K, k5) be its radius. Now, let Q be a convex (in interior sense) m-dimensional surface in T whose normal curvatures with respect to any normal are not greater than X satisfying 0 < X < K. Denote by LX the length of a circular arc of curvature X in P2(k3) with the distance 2RO between its ends. We prove that the volume of Q does not exceed the volume of a ball in Pm(k, (n m)X2) of radius 2 LXThese volumes are equal when T is a ball in Pn(k3) and Q is its m-dimensional diameter." @default.
- W2083379421 created "2016-06-24" @default.
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- W2083379421 date "1978-02-01" @default.
- W2083379421 modified "2023-09-25" @default.
- W2083379421 title "The volume of a slightly curved submanifold in a convex region" @default.
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- W2083379421 doi "https://doi.org/10.1090/s0002-9939-1978-0474147-6" @default.
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