Geodesic
The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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We show that the co-rays to a ray in a complete non-compact Finsler manifold contain geodesic segments to upper level sets of Busemann functions. Moreover, we characterise the co-point set to a ray as the cut locus of such level sets. The structure theorem of the co-point set on a surface, namely that is a local tree, and other properties follow immediately from the known results about the cut locus. We point out that some of our findings, in special the relation of co-point set to the upper lever sets, are new even for Riemannian manifolds.
Keywords: Finsler manifolds; ray; co-ray (asymptotic ray); cut locus; co-points; distance function; Busemann function. 
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     author = {Sorin V. Sabau},
     title = {The {Co-Points} of {Rays} are {Cut} {Points} of {Upper} {Level} {Sets} for {Busemann} {Functions}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a35/}
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Sorin V. Sabau. The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a35/

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