On the boundary of closed convex sets in Eⁿ

2013/01/04 by Beltagy, M., Shenawy, S.
#52A20 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1301.0688

Abstract

In this article a class of closed convex sets in the Euclidean n-space which are the convex hull of their profiles is described. Thus a generalization of Krein-Milman theorem\citeLay:1982 to a class of closed non-compact convex sets is obtained. Sufficient and necessary conditions for convexity, affinity and starshapedness of a closed set and its boundary have been derived in terms of their boundary points.

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