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@article{BUMI_2012_9_5_3_a5, author = {Ambrosio, Luigi and Gigli, Nicola and Savar\`e, Giuseppe}, title = {Heat {Flow} and {Calculus} on {Metric} {Measure} {Spaces} with {Ricci} {Curvature} {Bounded} {Below} - the {Compact} {Case}}, journal = {Bollettino della Unione matematica italiana}, pages = {575--629}, publisher = {mathdoc}, volume = {Ser. 9, 5}, number = {3}, year = {2012}, zbl = {1288.58016}, mrnumber = {3051737}, language = {en}, url = {http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_3_a5/} }
TY - JOUR AU - Ambrosio, Luigi AU - Gigli, Nicola AU - Savarè, Giuseppe TI - Heat Flow and Calculus on Metric Measure Spaces with Ricci Curvature Bounded Below - the Compact Case JO - Bollettino della Unione matematica italiana PY - 2012 SP - 575 EP - 629 VL - 5 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_3_a5/ LA - en ID - BUMI_2012_9_5_3_a5 ER -
%0 Journal Article %A Ambrosio, Luigi %A Gigli, Nicola %A Savarè, Giuseppe %T Heat Flow and Calculus on Metric Measure Spaces with Ricci Curvature Bounded Below - the Compact Case %J Bollettino della Unione matematica italiana %D 2012 %P 575-629 %V 5 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_3_a5/ %G en %F BUMI_2012_9_5_3_a5
Ambrosio, Luigi; Gigli, Nicola; Savarè, Giuseppe. Heat Flow and Calculus on Metric Measure Spaces with Ricci Curvature Bounded Below - the Compact Case. Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 3, pp. 575-629. http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_3_a5/
[1] User's guide to optimal transport theory, to appear. | DOI | MR
- ,[2]
- - - - , work in progress (2012).[3] Gradient flows in metric spaces and in the space of probability measures, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, second ed., 2008. | MR | Zbl
- - ,[4] Calculus and heat flow in metric measure spaces and applications to spaces with ricci bounds from below, Arxiv 1106.2090, (2011), 1-74. | MR
- - ,[5] Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces, Arxiv 1111.3730, (2011), 1-28. | DOI | MR
- - ,[6] Metric measure spaces with Riemannian Ricci curvature bounded from below, Arxiv 1109.0222, (2011), 1-60. | DOI | MR
- - ,[7] Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces, To appear on Ann. Mat. Pura Appl. (2012). | DOI | MR
- ,[8] 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
,[9] Differentiability of Lipschitz functions on metric measure spaces, Geom. Funct. Anal., 9 (1999), 428-517. | DOI | MR | Zbl
,[10] Eulerian calculus for the displacement convexity in the Wasserstein distance, SIAM J. Math. Anal., 40 (2008), 1104-1122. | DOI | MR | Zbl
- ,[11] Dirichlet forms and Markov processes, vol. 23 of North-Holland Mathematical Library, North-Holland Publishing Co., Amsterdam, 1980. | MR | Zbl
,[12] On the heat flow on metric measure spaces: existence, uniqueness and stability, Calc. Var. Partial Differential Equations, 39 (2010), 101-120. | DOI | MR | Zbl
,[13] On the differential structure of metric measure spaces and applications, Submitted paper, (2012). | DOI | MR | Zbl
,[14] Optimal maps in non branching spaces with Ricci curvature bounded from below, To appear on Geom. Funct. Anal., (2012). | DOI | MR | Zbl
,[15] Heat flow on Alexandrov spaces, To appear on Comm. Pure Appl. Math., (2012). | DOI | MR
- - ,[16] First variation formula in Wasserstein spaces over compact Alexandrov spaces, To appear on Canad. Math. Bull. | DOI | MR | Zbl
- ,[17] Nonsmooth calculus, Bull. Amer. Math. Soc. (N.S.), 44 (2007), 163-232. | DOI | MR
,[18] Quasiconformal maps in metric spaces with controlled geometry, Acta Math., 181 (1998), 1-61. | DOI | MR | Zbl
- ,[19] A note on Lipschitz functions, upper gradients, and the Poincaré inequality, New Zealand J. Math., 28 (1999), 37-42. | MR | Zbl
- ,[20] Quasiconformal mappings and Sobolev spaces, Studia Math., 131 (1998), 1-17. | fulltext EuDML | MR | Zbl
- ,[21] Duality on gradient estimates and wasserstein controls, Journal of Functional Analysis, 258 (2010), 3758-3774. | DOI | MR | Zbl
,[22] Characterization of absolutely continuous curves in Wasserstein spaces, Calc. Var. Partial Differential Equations, 28 (2007), 85-120. | DOI | MR | Zbl
,[23] Ricci curvature for metric-measure spaces via optimal transport, Ann. of Math. (2), 169 (2009), 903-991. | DOI | MR | Zbl
- ,[24] Finsler interpolation inequalities, Calc. Var. Partial Differential Equations, 36 (2009), 211-249. | DOI | MR
,[25] Gradient flows on Wasserstein spaces over compact Alexandrov spaces, Amer. J. Math., 131 (2009), 475-516. | DOI | MR | Zbl
,[26] Heat flow on Finsler manifolds, Comm. Pure Appl. Math., 62 (2009), 1386-1433. | DOI | MR | Zbl
- ,[27] Alexandrov meets lott-villani-sturm, arXiv:1003.5948v1, (2010). | MR | Zbl
,[28] Improved geodesics for the reduced curvature-dimension condition in branching metric spaces, Discrete Contin. Dyn. Syst., (2011). to appear. | DOI | MR
,[29] Gradient flows and evolution variational inequalities in metric spaces, In preparation, (2010).
,[30] Newtonian spaces: an extension of Sobolev spaces to metric measure spaces, Rev. Mat. Iberoamericana, 16 (2000), 243-279. | fulltext EuDML | DOI | MR | Zbl
,[31] On the geometry of metric measure spaces. I, Acta Math., 196 (2006), 65-131. | DOI | MR
,[32] Optimal transport. Old and new, vol. 338 of Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, Berlin, 2009. | DOI | MR | Zbl
,[33] Ricci curvature on Alexandrov spaces and rigidity theorems, Comm. Anal. Geom., 18 (2010), 503-553. | DOI | MR | Zbl
- ,