Geodesic
Some analytic properties of convex sets in Riemannian spaces
Sbornik. Mathematics, Tome 35 (1979) no. 3, pp. 333-350 Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate analytic properties of the boundary $bC$ of a locally convex set $C$ in a Riemannian space $M^n$, $n\geqslant2$, in particular, its mean curvature $H$ as a function of the set. For an $M^3$ of nonnegative curvature we prove the inequality $$ 4\pi\chi(bC)t_0\leq H(bC)+\Omega(C), $$ where $\chi$ is the Euler characteristic, $t_0$ the radius of the largest ball inscribed in $C$, and $\Omega(C)$ the scalar curvature of $C$. Bibliography: 16 titles. 
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     author = {S. V. Buyalo},
     title = {Some analytic properties of convex sets in {Riemannian} spaces},
     journal = {Sbornik. Mathematics},
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     volume = {35},
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     language = {en},
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S. V. Buyalo. Some analytic properties of convex sets in Riemannian spaces. Sbornik. Mathematics, Tome 35 (1979) no. 3, pp. 333-350. http://geodesic.mathdoc.fr/item/SM_1979_35_3_a2/

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