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- W4296883491 abstract "Let $mathcal{W}^{n}$ be the class of $C^{infty }$ complete simply connected $n-$dimensional manifolds without conjugate points. The hyperbolic space as well as Euclidean space are good examples of such manifolds. Let $% Win mathcal{W}^{n}$ and let $A$ be a subset of $W$. This article aims at characterization and building convex and starshaped sets in this class from inside. For example, it is proven that, for a compact starshaped set, the convex kernel is the intersection of stars of extreme points only. Also, if a closed unbounded convex set $A$ does not contain a totally geodesic hypersurface and its boundary has no geodesic ray, then $A$ is the convex hull of its extreme points. This result is a refinement of the well-known Karein-Millman theorem." @default.
- W4296883491 created "2022-09-24" @default.
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- W4296883491 date "2013-11-03" @default.
- W4296883491 modified "2023-09-26" @default.
- W4296883491 title "Convex and starshaped sets in manifolds without conjugate points" @default.
- W4296883491 doi "https://doi.org/10.48550/arxiv.1311.0454" @default.
- W4296883491 hasPublicationYear "2013" @default.
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