Geodesic
Sufficient conditions for convexity in manifolds without focal points
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 3, pp. 443-449.

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In this paper, local, global, strongly local and strongly global supportings of subsets in a complete simply connected smooth Riemannian manifold without focal points are defined. Sufficient conditions for convexity of subsets in the same sort of manifolds have been derived in terms of the above mentioned types of supportings.
Classification : 53C20, 53C42
Keywords: supporting of subsets; convex subsets (hypersurfaces); conjugate (focal) points; horospheres 
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     author = {Beltagy, M.},
     title = {Sufficient conditions for convexity in manifolds without focal points},
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     pages = {443--449},
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     number = {3},
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     zbl = {0797.53034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1993__34_3_a6/}
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Beltagy, M. Sufficient conditions for convexity in manifolds without focal points. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 3, pp. 443-449. http://geodesic.mathdoc.fr/item/CMUC_1993__34_3_a6/