[1] Anderson M. On the topology of complete manifolds of non-negative Ricci curvature. Topology, 1990, 29(1): 41--55
[2] Burago D, Burago Y, Ivanov S. A Course in Metric Geometry. Graduate Studies in Mathematics, Vol 33. Amer Math Soc, 2001
[3] Burago Y, Gromov M, Perelman G. A. D. Alexandrov spaces with curvatures bounded below. Russian Math Surveys, 1992, 47: 1--58
[4] Bacher, K, Sturm K. Localization and tensorization properties of the Curvature-Dimension condition for metric measure mpaces. J Funct Anal, 2010, 259(1): 28--56
[5] Chavel I. Riemannian Geometry---A Modern Introduction. 2nd ed. Cambridge: Cambridge University Press, 2006
[6] Cheeger J. Degeneration of Riemannian metrics under Ricci curvature bounds. Lezione Fermiane, Accademia Nazionale dei Lincei, Scuola Normale Superiore, Pisa, 2001
[7] Cheeger J, Colding T. Lower bounds on Ricci curvature and the almost rigidity of warped products. Ann Math, 1996, 144: 189--237
[8] Cheeger J, Colding T. On the structure of spaces with Ricci curvature bounded below I, II, III. J Differential Geom, 1997, 46: 406--480; 2000, 54: 13--35;
2000, 54: 37--74
[9] Colding T, Minicozzi II W. Harmonic functions on manifolds. Ann Math, 1997, 146: 725--747
[10] Colding T, Minicozzi II W. Weyl type bounds for harmonic functions. Invent Math, 1998, 131: 257--298
[11] Cordero-Erausquin D, McCann R J, Schmuckenschläger M. A Riemannian interpolation inequality à la Borell, Brascamp and Lieb. Invent Math, 2001, 146: 219--257
[12] Hua B. Generalized Liouville theorem in nonnegatively curved Alexandrov space. Chin Ann Math Ser B, 2009, 30(2): 111--128
[13] Heinonen J. Lectures on Analysis on Metric Spaces. Springer-Verlag, 2001
[14] Kuwae K, Machigashira Y, Shioya T. Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces. Math Z, 2001, 238(2): 269--316
[15] Korevaar N, Schoen R. Sobolev spaces and harmonic maps for metric space targets. Comm Anal Geom, 1993, 1: 561--659
[16] Kuwae K, Shioya T. Laplacian comparison for Alexandrov spaces. http://cn.arxiv.org/abs/0709.0788v1
[17] Kuwae K, Shioya T. A topological splitting theorem for weighted Alexandrov spaces. http://cn.arxiv. org/abs/0903.5150v1
[18] Kuwae K, Shioya T. On generalized measure contraction property and energy functionals over Lipschitz maps. ICPA98 (Hammamet), Potential Anal, 2001, 15(1/2): 105--121
[19] Kuwae K, Shioya T. Sobolev and Dirichlet spaces over maps between metric spaces. J Reine Angew Math, 2003, 555: 39--75
[20] Kuwae K, Shioya T. Infinitesimal Bishop-Gromov condition for Alexandrov spaces//Probabilistic Approach to Geometry. Adv Stud Prue Math 57. Tokyo: Math Soc Japan, 2010: 293--302
[21] Li P. Harmonic sections of polynomial growth. Math Res Lett, 1997, 4: 35--44
[22] Lin F H. Analysis on singular spaces//Collection of Papers on Geometry, Analysis and Mathematical Physics. River Edge, NJ: World Sci Publ, 1997: 114--126
[23] Lin Y, Yau S T. Ricci curvature and eigenvalue estimate on locally finite graph. Math Res Lett, 2010, 17(2): 345--358
[24] Lott J, Villani C. Ricci curvature for metric-measure spaces via optimal transport. Ann Math, 2009, 169: 903--991
[25] Lott J, Villani C. Weak curvature bounds and functional inequalities. J Funct Anal, 2007, 245(1): 311--333
[26] Mashiko Y. A splitting theorem for Alexandrov spaces. Pacific J Math, 2002, 204: 445--458
[27] Ohta S. On measure contraction property of metric measure spaces. Comment Math Helvetici, 2007, 82(4): 805--828
[28] Ohta S. Products, cones, and suspensions of spaces with the measure comtraction property. J London Math Soc, 2007: 1--12
[29] Ohta S. Finsler interpolation inequalities. Calc Var Partial Differ Equ, 2009, 36(2): 211--249
[30] Otsu Y, Shioya T. The Riemannian structure of Alexandrov spaces. J Differ Geom, 1994, 39: 629--658
[31] Petersen P. Riemannian Geometry. Graduate Texts in Mathematics, Vol 171. 2nd Ed. Springer, 2006
[32] Perelman G. Elements of Morse theory on Aleksandrov spaces. St Petersbg Math J, 1993, 5(1): 205--213
[33] Perelman G. DC structure on Alexandrov spaces. Preprint, preliminary version available online at www.math.psu.edu/petrunin/
[34] Perelman G, Petrunin A.Quasigeodesics and gradient curves in Alexandrov spaces. Preprint, available online at www.math.psu.edu/petrunin/
[35] Petrunin A. Parallel transportation for Alexandrov spaces with curvature bounded below. Geom Funct Analysis, 1998, 8(1): 123-148
[36] Petrunin A. Alexandrov meets Lott--Villani--Sturm. Preprint (2009), available online at www.math.psu. edu/petrunin/
[37] Petrunin A. Semiconcave Functions in Alexandrov's Geometry. Surveys in Differential Geometry XI.
[38] Petrunin A. Harmonic functions on Alexandrov space and its applications. ERA American Mathematical Society, 2003, 9: 135--141
[39] Ranjbar-Motlagh A. On the Poincer\'e inequality for abstract spaces. Bull Austral Math Soc, 2005, 71: 193--204
[40] von Renesse M. Local Poincarè via transportation. Math Z, 2008, 259: 21--31
[41] von Renesse M, Sturm K. Transport inequalities, gradient estimates, entropy, and Ricci curvature. Comm Pure Appl Math, 2005, 58: 923--940
[42] Schoen R, Yau S T. Lectures on Differential Geometry. International Press, 1994
[43] Sturm K. On the geometry of metric measure spaces I, II. Acta Math, 2006, 196(1): 65--177
[44] Sturm K. Diffusion processes and heat kernels on metric spaces. Ann Probab, 1998, 26: 1--55
[45] Sturm K. Analysis on local Dirichlet spaces. III. The parabolic Harnack inequality. J Math Pure Appl, 1996, 75(3): 273--297
[46] Sturm K. Convex functionals of probability measures and nonlinear diffusions on manifolds. J Math Pures Appl, 2005, 84(9): 149--168
[47] Villani C. Optimal Transport, Old and New. Grundlehren der mathematischen Wissenschaften, Vol 338. Springer, 2008
[48] Yau S T. Nonlinear analysis in geometry. L'Enseignement Math\'ematique, S\'erie des conf\'erences de l'Union Math\'emathique Internationale, No. 8, SRO--KUNDIG, Genève, 1986
[49] Zhang H C, Zhu X P. Ricci curvature on Alexandrov spaces and rigidity theorems. http://arxiv.org/abs/ 0912.3190.
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