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Supporting Function in Riemannian Manifolds without Focal Points
M. Beltagy ...et al KYUNGPOOK UNIVERSITY 1997 Kyungpook mathematical journal Vol.37 No.1
In this paper the Busemann function in a complete simply connected smooth Riemannian manifold ŵ without focal points is used to define a supporting function for hypersurfaces of ŵ. This last function is used to derive a necessary and suffcient condition fora closed hypersurface of ŵ to be a geodesic sphere.
On Convex and Starshaped Hulls
M. Beltagy ...et al KYUNGPOOK UNIVERSITY 2000 Kyungpook mathematical journal Vol.40 No.2
This paper deals with the two main geometric concepts, convexity as well as star-shapedness, of subsets of Euclidean spaces. The concept of starshaped hull is introduced and studied from the geometric point of view. Additional geometric properties of convex hulls are established. Interesting examples are given to illustrate the obtained results.