Finite-dimensional Busemann spaces with non-negative curvature satisfying Ohta's S-concavity and local semi-convexity admit non-trivial integer-dimensional Hausdorff measure, satisfy the measure contraction property, are rectifiable, and have unique finite-dimensional Banach tangent cones at almost-
A Toponogov type triangle comparison theorem in Finsler geometry
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The aim of this article is to establish a Toponogov type triangle comparison theorem for Finsler manifolds, in the manner of radial curvature geometry. We consider the situation that the radial flag curvature is bounded below by the radial curvature function of a non-compact surface of revolution, the edge opposite to the base point is contained in a Berwald-like region, and that the Finsler metric is convex enough in the radial directions in that region.
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On the Structure of Busemann Spaces with Non-Negative Curvature
Finite-dimensional Busemann spaces with non-negative curvature satisfying Ohta's S-concavity and local semi-convexity admit non-trivial integer-dimensional Hausdorff measure, satisfy the measure contraction property, are rectifiable, and have unique finite-dimensional Banach tangent cones at almost-