摘要: We investigate barycenters of probability measures on proper Alexandrov spaces curvature bounded below, and show that they enjoy several properties relevant to or different from those in metric above. prove the reverse variance inequality, push forward a measure tangent cone at its barycenter has flat support.
sci-hub.se 参考文章(23)
Takumi Yokota, A rigidity theorem in Alexandrov spaces with lower curvature bound Mathematische Annalen. ,vol. 353, pp. 305- 331 ,(2012) , 10.1007/S00208-011-0686-8
John Lott, Cedric Villani, Ricci curvature for metric-measure spaces via optimal transport Annals of Mathematics. ,vol. 169, pp. 903- 991 ,(2009) , 10.4007/ANNALS.2009.169.903
Karl-Theodor Sturm, A Semigroup Approach to Harmonic Maps Potential Analysis. ,vol. 23, pp. 225- 277 ,(2005) , 10.1007/S11118-004-7740-Z
Stephanie Halbeisen, On tangent cones of Alexandrov spaces with curvature bounded below Manuscripta Mathematica. ,vol. 103, pp. 169- 182 ,(2000) , 10.1007/S002290070018
Ayato Mitsuishi, A splitting theorem for infinite dimensional Alexandrov spaces with nonnegative curvature and its applications Geometriae Dedicata. ,vol. 144, pp. 101- 114 ,(2010) , 10.1007/S10711-009-9390-1
Karl-Theodor Sturm, On the geometry of metric measure spaces. II Acta Mathematica. ,vol. 196, pp. 133- 177 ,(2006) , 10.1007/S11511-006-0003-7
A D Aleksandrov, V N Berestovskii, I G Nikolaev, Generalized Riemannian spaces Russian Mathematical Surveys. ,vol. 41, pp. 1- 54 ,(1986) , 10.1070/RM1986V041N03ABEH003311
Shin-ichi Ohta, Uniform convexity and smoothness, and their applications in Finsler geometry Mathematische Annalen. ,vol. 343, pp. 669- 699 ,(2009) , 10.1007/S00208-008-0286-4
Yu Burago, M Gromov, G Perel'man, A.D. Alexandrov spaces with curvature bounded below(1) Russian Mathematical Surveys. ,vol. 47, pp. 1- 58 ,(1992) , 10.1070/RM1992V047N02ABEH000877
Shin-ichi Ohta, Extending Lipschitz and Holder maps between metric spaces Positivity. ,vol. 13, pp. 407- 425 ,(2009) , 10.1007/S11117-008-2202-2