Geodesic
An estimate from below for the spatial diameter of a surface in terms of its intrinsic radius and curvature
Sbornik. Mathematics, Tome 15 (1971) no. 3, pp. 405-414 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we prove the following Theorem. Let $F$ be a regular simply connected surface of class $C^3$ in $R^3$. There exist postitive absolute constants $C$ and $C_1$ such that if $$ \mu=\int_F|K|\,dS<C, $$ where $K$ is the Gaussian curvature and $S$ is the area element on $F$, the estimate $$ d\geqslant\bigl(\sqrt3-C_1\sqrt\mu\bigr)r $$ holds. Bibliography: 11 titles. 
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Yu. D. Burago. An estimate from below for the spatial diameter of a surface in terms of its intrinsic radius and curvature. Sbornik. Mathematics, Tome 15 (1971) no. 3, pp. 405-414. http://geodesic.mathdoc.fr/item/SM_1971_15_3_a2/

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