- The Co-Factors of Rays are Minimize Factors of Higher Stage Units for Busemann Capabilities(arXiv)
Creator : Sorin V. Sabau
Summary : : We present that the co-rays to a ray in an entire non-compact Finsler manifold comprise geodesic segments to higher stage units of Busemann capabilities. Furthermore, we characterise the co-point set to a ray because the minimize locus of such stage units. The construction theorem of the co-point set on a floor, specifically that may be a native tree, and different properties comply with instantly from the identified outcomes in regards to the minimize locus. We level out that a few of our findings, in particular the relation of co-point set to the higher lever units, are new even for Riemannian manifolds.
2. Busemann capabilities and barrier capabilities(arXiv)
Creator : Xiaojun Cui, Jian cheng
Summary : We present that Busemann capabilities on a clean, non-compact, full, boundaryless, linked Riemannian manifold are viscosity options with respect to the Hamilton-Jacobi equation decided by the Riemannian metric and consequently they’re domestically semi-concave with linear modulus. We additionally evaluation the construction of singularity units of Busemann capabilities. Furthermore we research barrier capabilities, that are analogues to Mather’s barrier capabilities in Mather principle, and supply some basic properties. Primarily based on barrier capabilities, we might outline some relations on the set of strains and thus classify them. We additionally focus on some preliminary relations with the best boundary of the Riemannian manifold