Barycenters in Alexandrov spaces of curvature bounded below
نویسنده
چکیده
We investigate barycenters of probability measures on proper Alexandrov spaces of curvature bounded below, and show that they enjoy several properties relevant to or different from those in metric spaces of curvature bounded above. We prove the reverse variance inequality, and show that the push forward of a measure to the tangent cone at its barycenter has the flat support.
منابع مشابه
Differential Geometric Aspects of Alexandrov Spaces
We summarize the results on the differential geometric structure of Alexandrov spaces developed in [Otsu and Shioya 1994; Otsu 1995; Otsu and Tanoue a]. We discuss Riemannian and second differentiable structure and Jacobi fields on Alexandrov spaces of curvature bounded below or above.
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