Ambrosio, Gigli, Savarè: Heat Flow and Calculus on Metric Measure Spaces with Ricci Curvature Bounded Below

Ambrosio, Luigi and Gigli, Nicola and Savarè, Giuseppe:
Heat Flow and Calculus on Metric Measure Spaces with Ricci Curvature Bounded Below - the Compact Case
Bollettino dell'Unione Matematica Italiana Serie 9 5 (2012), fasc. n.3, p. 575-629, (English)
pdf (585 Kb), djvu (534 Kb). | MR 3051737 | Zbl 1288.58016

Referenze Bibliografiche

[1] L. AMBROSIO - N. GIGLI, User's guide to optimal transport theory, to appear. | fulltext (doi) | MR 3050280

[2] L. AMBROSIO - N. GIGLI - A. MONDINO - G. SAVARÉ - T. RAJALA, work in progress (2012).

[3] L. AMBROSIO - N. GIGLI - G. SAVARÉ, Gradient flows in metric spaces and in the space of probability measures, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, second ed., 2008. | MR 2401600 | Zbl 1145.35001

[4] L. AMBROSIO - N. GIGLI - G. SAVARÉ, Calculus and heat flow in metric measure spaces and applications to spaces with ricci bounds from below, Arxiv 1106.2090, (2011), 1-74. | MR 3060497

[5] L. AMBROSIO - N. GIGLI - G. SAVARÉ , Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces, Arxiv 1111.3730, (2011), 1-28. | fulltext (doi) | MR 3090143

[6] L. AMBROSIO - N. GIGLI - G. SAVARÉ , Metric measure spaces with Riemannian Ricci curvature bounded from below, Arxiv 1109.0222, (2011), 1-60. | fulltext (doi) | MR 3205729

[7] L. AMBROSIO - T. RAJALA, Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces, To appear on Ann. Mat. Pura Appl. (2012). | fulltext (doi) | MR 3158838

[8] H. BRÉZIS, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland Publishing Co., Amsterdam, 1973. North-Holland Mathematics Studies, No. 5. Notas de Matemática (50). | Zbl 0252.47055

[9] J. CHEEGER, Differentiability of Lipschitz functions on metric measure spaces, Geom. Funct. Anal., 9 (1999), 428-517. | fulltext (doi) | MR 1708448 | Zbl 0942.58018

[10] S. DANERI - G. SAVARÉ, Eulerian calculus for the displacement convexity in the Wasserstein distance, SIAM J. Math. Anal., 40 (2008), 1104-1122. | fulltext (doi) | MR 2452882 | Zbl 1166.58011

[11] M. FUKUSHIMA, Dirichlet forms and Markov processes, vol. 23 of North-Holland Mathematical Library, North-Holland Publishing Co., Amsterdam, 1980. | MR 569058 | Zbl 0422.31007

[12] N. GIGLI, On the heat flow on metric measure spaces: existence, uniqueness and stability, Calc. Var. Partial Differential Equations, 39 (2010), 101-120. | fulltext (doi) | MR 2659681 | Zbl 1200.35178

[13] N. GIGLI, On the differential structure of metric measure spaces and applications, Submitted paper, (2012). | fulltext (doi) | MR 3381131 | Zbl 1325.53054

[14] N. GIGLI, Optimal maps in non branching spaces with Ricci curvature bounded from below, To appear on Geom. Funct. Anal., (2012). | fulltext (doi) | MR 2984123 | Zbl 1257.53055

[15] N. GIGLI - K. KUWADA - S. OHTA, Heat flow on Alexandrov spaces, To appear on Comm. Pure Appl. Math., (2012). | fulltext (doi) | MR 3008226

[16] N. GIGLI - S.-I. OHTA, First variation formula in Wasserstein spaces over compact Alexandrov spaces, To appear on Canad. Math. Bull. | fulltext (doi) | MR 2994677 | Zbl 1264.53050

[17] J. HEINONEN, Nonsmooth calculus, Bull. Amer. Math. Soc. (N.S.), 44 (2007), 163-232. | fulltext (doi) | MR 2291675

[18] J. HEINONEN - P. KOSKELA, Quasiconformal maps in metric spaces with controlled geometry, Acta Math., 181 (1998), 1-61. | fulltext (doi) | MR 1654771 | Zbl 0915.30018

[19] J. HEINONEN - P. KOSKELA, A note on Lipschitz functions, upper gradients, and the Poincaré inequality, New Zealand J. Math., 28 (1999), 37-42. | MR 1691958 | Zbl 1015.46020

[20] P. KOSKELA - P. MACMANUS, Quasiconformal mappings and Sobolev spaces, Studia Math., 131 (1998), 1-17. | fulltext EuDML | MR 1628655 | Zbl 0918.30011

[21] K. KUWADA, Duality on gradient estimates and wasserstein controls, Journal of Functional Analysis, 258 (2010), 3758-3774. | fulltext (doi) | MR 2606871 | Zbl 1194.53032

[22] S. LISINI, Characterization of absolutely continuous curves in Wasserstein spaces, Calc. Var. Partial Differential Equations, 28 (2007), 85-120. | fulltext (doi) | MR 2267755 | Zbl 1132.60004

[23] J. LOTT - C. VILLANI, Ricci curvature for metric-measure spaces via optimal transport, Ann. of Math. (2), 169 (2009), 903-991. | fulltext (doi) | MR 2480619 | Zbl 1178.53038

[24] S.-I. OHTA, Finsler interpolation inequalities, Calc. Var. Partial Differential Equations, 36 (2009), 211-249. | fulltext (doi) | MR 2546027

[25] S.-I. OHTA, Gradient flows on Wasserstein spaces over compact Alexandrov spaces, Amer. J. Math., 131 (2009), 475-516. | fulltext (doi) | MR 2503990 | Zbl 1169.53053

[26] S.-I. OHTA - K.-T. STURM, Heat flow on Finsler manifolds, Comm. Pure Appl. Math., 62 (2009), 1386-1433. | fulltext (doi) | MR 2547978 | Zbl 1176.58012

[27] A. PETRUNIN, Alexandrov meets lott-villani-sturm, arXiv:1003.5948v1, (2010). | MR 2869253 | Zbl 1247.53038

[28] T. RAJALA, Improved geodesics for the reduced curvature-dimension condition in branching metric spaces, Discrete Contin. Dyn. Syst., (2011). to appear. | fulltext (doi) | MR 3007737

[29] G. SAVARÉ , Gradient flows and evolution variational inequalities in metric spaces, In preparation, (2010).

[30] N. SHANMUGALINGAM, Newtonian spaces: an extension of Sobolev spaces to metric measure spaces, Rev. Mat. Iberoamericana, 16 (2000), 243-279. | fulltext EuDML | fulltext (doi) | MR 1809341 | Zbl 0974.46038

[31] K.-T. STURM, On the geometry of metric measure spaces. I, Acta Math., 196 (2006), 65-131. | fulltext (doi) | MR 2237206

[32] C. VILLANI, Optimal transport. Old and new, vol. 338 of Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, Berlin, 2009. | fulltext (doi) | MR 2459454 | Zbl 1156.53003

[33] H.-C. ZHANG - X.-P. ZHU, Ricci curvature on Alexandrov spaces and rigidity theorems, Comm. Anal. Geom., 18 (2010), 503-553. | fulltext (doi) | MR 2747437 | Zbl 1230.53064

bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Referenze Bibliografiche