On the geometry of metric measure spaces. II
Tóm tắt
Từ khóa
Tài liệu tham khảo
Ambrosio, L., Tilli, P.: Topics on Analysis in Metric Spaces. Oxford Lecture Series in Mathematics and its Applications, 25. Oxford University Press, Oxford (2004)
Bakry, D., Émery, M.: Diffusions hypercontractives. In: Séminaire de probabilités, XIX, 1983/84. Lecture Notes in Math., 1123, pp. 177–206. Springer, Berlin (1985)
Bakry, D., Qian, Z.: Some new results on eigenvectors via dimension, diameter, and Ricci curvature. Adv. Math. 155, 98–153 (2000)
Chavel, I.: Riemannian Geometry—a Modern Introduction. Cambridge Tracts in Mathematics, 108. Cambridge University Press, Cambridge (1993)
Cheeger, J.: Differentiability of Lipschitz functions on metric measure spaces. Geom. Funct. Anal. 9, 428–517 (1999)
Cordero-Erausquin, D., McCann, R.J., Schmuckenschläger, M.: A Riemannian interpolation inequality à la Borell, Brascamp and Lieb. Invent. Math. 146, 219–257 (2001)
Gromov, M.: Metric Structures for Riemannian and non-Riemannian Spaces. Progress in Mathematics, 152. Birkhäuser Boston, Boston, MA (1999)
Korevaar, N.J., Schoen, R.M.: Sobolev spaces and harmonic maps for metric space targets. Comm. Anal. Geom. 1, 561–659 (1993)
Kuwae, K., Shioya, T.: On generalized measure contraction property and energy functionals over Lipschitz maps. Potential Anal. 15, 105–121 (2001)
Kuwae, K., Shioya, T.: Sobolev and Dirichlet spaces over maps between metric spaces. J. Reine Angew. Math. 555, 39–75 (2003)
Lott, J., Villani, C.: Ricci curvature for metric-measure spaces via optimal transport. Preprint (2005)
Lott J., Villani, C.: Weak curvature conditions and Poincaré inequalities. Preprint (2005)
von Renesse, M.-K.: Local Poincaré via transportation. To appear in Math. Z
Sturm, K.-T.: Analysis on local Dirichlet spaces. III. The parabolic Harnack inequality. J. Math. Pures Appl. 75, 273–297 (1996)
Sturm, K.-T.: Convex functionals of probability measures and nonlinear diffusions on manifolds. J. Math. Pures Appl. 84, 149–168 (2005)
Sturm, K.-T.: A curvature-dimension condition for metric measure spaces. C. R. Math. Acad. Sci. Paris 342, 197–200 (2006)