-
2
-
-
33746157912
-
Gradient flows in metric spaces and in the space of probability measures
-
Birkhaüser, Basel
-
L. Ambrosio, N. Gigli, and G. Savarè, Gradient flows in metric spaces and in the space of probability measures, Lectures in Mathematics ETH Zürich, Birkhaüser, Basel (2005).
-
(2005)
Lectures in Mathematics ETH Zürich
-
-
Ambrosio, L.1
Gigli, N.2
Savarè, G.3
-
3
-
-
84887242052
-
Gradient flows with metric and differentiable structures, and applications to the Wasserstein space
-
L. Ambrosio, N. Gigli, and G. Savarè, Gradient flows with metric and differentiable structures, and applications to the Wasserstein space, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 15 (2004), 327-343.
-
(2004)
Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl.
, vol.15
, pp. 327-343
-
-
Ambrosio, L.1
Gigli, N.2
Savarè, G.3
-
4
-
-
7244240248
-
Sur les inégalités de Sobolev logarithmiques
-
Société Mathématique de France, Paris
-
C. Ané, S. Blachère, D. Chafaï, P. Fougères, I. Gentil, F. Malrieu, C. Roberto, and G. Scheffer, Sur les inégalités de Sobolev logarithmiques, Panoramas et Synthèses 10, Société Mathématique de France, Paris (2000).
-
(2000)
Panoramas et Synthèses
, vol.10
-
-
Ané, C.1
Blachère, S.2
Chafaï, D.3
Fougères, P.4
Gentil, I.5
Malrieu, F.6
Roberto, C.7
Scheffer, G.8
-
5
-
-
0002925263
-
L'hypercontractivité et son utilisation en théorie des semigroupes
-
Springer-Verlag, New York
-
D. Bakry, L'hypercontractivité et son utilisation en théorie des semigroupes, in Lectures on Probability Theory (Saint-Flour, 1992), Lecture Notes in Math. 1581 (1994), 1-114, Springer-Verlag, New York.
-
(1994)
Lectures on Probability Theory (Saint-Flour, 1992), Lecture Notes in Math
, vol.1581
, pp. 1-114
-
-
Bakry, D.1
-
6
-
-
0001119849
-
Diffusions hypercontractives
-
Springer-Verlag, New York
-
D. Bakry and M. Émery, Diffusions hypercontractives, in Séminaire de Probabilités XIX, Lecture Notes in Math. 1123 (1985), 177-206, Springer-Verlag, New York.
-
(1985)
Séminaire de Probabilités XIX, Lecture Notes in Math
, vol.1123
, pp. 177-206
-
-
Bakry, D.1
Émery, M.2
-
7
-
-
33845497931
-
Optimal mass transportation and Mather theory
-
P. Bernard and B. Buffoni, Optimal mass transportation and Mather theory, J. of European Math. Soc. 9 (2007), 85-121.
-
(2007)
J. of European Math. Soc.
, vol.9
, pp. 85-121
-
-
Bernard, P.1
Buffoni, B.2
-
8
-
-
0035638785
-
Hypercontractivity of Hamilton-Jacobi equations
-
S. Bobkov, I. Gentil, and M. Ledoux, Hypercontractivity of Hamilton-Jacobi equations, J. Math. Pures Appl. 80 (2001), 669-696.
-
(2001)
J. Math. Pures Appl.
, vol.80
, pp. 669-696
-
-
Bobkov, S.1
Gentil, I.2
Ledoux, M.3
-
9
-
-
0002829137
-
Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
-
S. Bobkov and F. Götze, Exponential integrability and transportation cost related to logarithmic Sobolev inequalities, J. Funct. Anal. 163 (1999), 1-28.
-
(1999)
J. Funct. Anal.
, vol.163
, pp. 1-28
-
-
Bobkov, S.1
Götze, F.2
-
10
-
-
0033483717
-
Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations
-
Y. Brenier, Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations, Comm. Pure Appl. Math. 52 (1999), 411-452.
-
(1999)
Comm. Pure Appl. Math.
, vol.52
, pp. 411-452
-
-
Brenier, Y.1
-
11
-
-
0003365247
-
A Course in Metric Geometry
-
Amer. Math. Soc., Providence, RI
-
D. Burago, Y. Burago, and S. Ivanov, A Course in Metric Geometry, Graduate Studies in Mathematics 33, Amer. Math. Soc., Providence, RI, 2001.
-
(2001)
Graduate Studies in Mathematics
, vol.33
-
-
Burago, D.1
Burago, Y.2
Ivanov, S.3
-
12
-
-
33646864986
-
spaces with curvatures bounded below
-
Y. Burago, M. Gromov, and G. Perelman, A. D. Aleksandrov spaces with curvatures bounded below, Russian Math. Surveys 47 (1992), 1-58.
-
(1992)
Russian Math. Surveys
, vol.47
, pp. 1-58
-
-
Burago, Y.1
Gromov, M.2
Perelman, G.3
Aleksandrov, A.D.4
-
13
-
-
1842789036
-
One-dimensional variational problems
-
Oxford University Press, New York
-
G. Buttazzo, M. Giaquinta, and S. Hildebrandt, One-dimensional variational problems, Oxford Lecture Series in Mathematics and its Applications 15, Oxford University Press, New York (1998).
-
(1998)
Oxford Lecture Series in Mathematics and its Applications
, vol.15
-
-
Buttazzo, G.1
Giaquinta, M.2
Hildebrandt, S.3
-
14
-
-
32544445429
-
Contractions in the 2-Wasserstein length space and thermalization of granular media
-
J. A. Carrillo, R. J. McCann, and C. Villani, Contractions in the 2-Wasserstein length space and thermalization of granular media, Arch. Rational Mech. Anal. 179 (2006), 217-263.
-
(2006)
Arch. Rational Mech. Anal.
, vol.179
, pp. 217-263
-
-
Carrillo, J.A.1
McCann, R.J.2
Villani, C.3
-
15
-
-
0030522764
-
Lower bounds on Ricci curvature and the almost rigidity of warped products
-
J. Cheeger and T. Colding, Lower bounds on Ricci curvature and the almost rigidity of warped products, Ann. of Math. 144 (1996), 189-237.
-
(1996)
Ann. of Math.
, vol.144
, pp. 189-237
-
-
Cheeger, J.1
Colding, T.2
-
16
-
-
0031182532
-
On the structure of spaces with Ricci curvature bounded below I
-
J. Cheeger and T. Colding, On the structure of spaces with Ricci curvature bounded below I, J. Diff. Geom. 46 (1997), 406-480.
-
(1997)
J. Diff. Geom.
, vol.46
, pp. 406-480
-
-
Cheeger, J.1
Colding, T.2
-
17
-
-
0037887842
-
On the structure of spaces with Ricci curvature bounded below II
-
J. Cheeger and T. Colding, On the structure of spaces with Ricci curvature bounded below II, J. Diff. Geom. 54 (2000), 13-35.
-
(2000)
J. Diff. Geom.
, vol.54
, pp. 13-35
-
-
Cheeger, J.1
Colding, T.2
-
18
-
-
0002157976
-
On the structure of spaces with Ricci curvature bounded below III
-
J. Cheeger and T. Colding, On the structure of spaces with Ricci curvature bounded below III, J. Diff. Geom. 54 (2000), 37-74.
-
(2000)
J. Diff. Geom.
, vol.54
, pp. 37-74
-
-
Cheeger, J.1
Colding, T.2
-
19
-
-
0035602628
-
A Riemannian interpolation inequality à la Borell, Brascamp and Lieb
-
D. Cordero-Erausquin, R. McCann, and M. Schmuckenschläger, A Riemannian interpolation inequality à la Borell, Brascamp and Lieb, Invent. Math. 146 (2001), 219-257.
-
(2001)
Invent. Math.
, vol.146
, pp. 219-257
-
-
Cordero-Erausquin, D.1
McCann, R.2
Schmuckenschläger, M.3
-
20
-
-
67650039933
-
Prékopa-Leindler type inequalities on Riemannian manifolds, Jacobi fields, and optimal transport
-
D. Cordero-Erausquin, R. McCann, and M. Schmuckenschläger, Prékopa-Leindler type inequalities on Riemannian manifolds, Jacobi fields, and optimal transport, Ann. Fac. Sci. Toulouse Math. 15 (2006), 613-635.
-
(2006)
Ann. Fac. Sci. Toulouse Math.
, vol.15
, pp. 613-635
-
-
Cordero-Erausquin, D.1
McCann, R.2
Schmuckenschläger, M.3
-
21
-
-
0040460272
-
Collapsing of Riemannian manifolds and eigenvalues of Laplace operator
-
K. Fukaya, Collapsing of Riemannian manifolds and eigenvalues of Laplace operator, Invent. Math. 87 (1987), 517-547.
-
(1987)
Invent. Math.
, vol.87
, pp. 517-547
-
-
Fukaya, K.1
-
22
-
-
51649160427
-
Groups of polynomial growth and expanding maps
-
M. Gromov, Groups of polynomial growth and expanding maps, Publ. Math. de l'IHES 53 (1981), 53-78.
-
(1981)
Publ. Math. de l'IHES
, vol.53
, pp. 53-78
-
-
Gromov, M.1
-
23
-
-
0003268230
-
Metric structures for Riemannian and non-Riemannian spaces
-
Birkhäuser, Boston
-
M. Gromov, Metric structures for Riemannian and non-Riemannian spaces, Prog. in Math. 152 (1999), Birkhäuser, Boston.
-
(1999)
Prog. in Math.
, vol.152
-
-
Gromov, M.1
-
24
-
-
84972492371
-
Manifolds near the boundary of existence
-
K. Grove and P. Petersen, Manifolds near the boundary of existence, J. Diff. Geom. 33 (1991), 379-394.
-
(1991)
J. Diff. Geom.
, vol.33
, pp. 379-394
-
-
Grove, K.1
Petersen, P.2
-
25
-
-
0032343437
-
The variational formulation of the Fokker-Planck equation
-
R. Jordan, D. Kinderlehrer, and F. Otto, The variational formulation of the Fokker-Planck equation, SIAM J. Math. Anal. 29 (1998), 1-17.
-
(1998)
SIAM J. Math. Anal.
, vol.29
, pp. 1-17
-
-
Jordan, R.1
Kinderlehrer, D.2
Otto, F.3
-
26
-
-
0000458262
-
Concentration of measure and logarithmic Sobolev inequalities
-
Springer-Verlag, New York
-
M. Ledoux, Concentration of measure and logarithmic Sobolev inequalities, Séminaire de Probabilités XXXIII, Lecture Notes in Mathematics 1709 (1999), 120-216, Springer-Verlag, New York.
-
(1999)
Séminaire de Probabilités XXXIII, Lecture Notes in Mathematics
, vol.1709
, pp. 120-216
-
-
Ledoux, M.1
-
29
-
-
0011869464
-
Convex statistical distances
-
BSB B. G. Teubner Verlagsgesellschaft, Leipzig
-
F. Liese and I. Vajda, Convex statistical distances, Teubner-Texte zur Mathematik 95, BSB B. G. Teubner Verlagsgesellschaft, Leipzig (1987).
-
(1987)
Teubner-Texte zur Mathematik
, vol.95
-
-
Liese, F.1
Vajda, I.2
-
30
-
-
0242350976
-
Some geometric properties of the Bakry-Émery-Ricci tensor
-
J. Lott, Some geometric properties of the Bakry-Émery-Ricci tensor, Comment. Math. Helv. 78 (2003), 865-883.
-
(2003)
Comment. Math. Helv.
, vol.78
, pp. 865-883
-
-
Lott, J.1
-
31
-
-
0031161793
-
A convexity principle for interacting gases
-
R. J. McCann, A convexity principle for interacting gases, Adv. Math. 128 (1997), 153- 179.
-
(1997)
Adv. Math.
, vol.128
, pp. 153-179
-
-
McCann, R.J.1
-
32
-
-
0035618489
-
Polar factorization of maps on Riemannian manifolds
-
R. J. McCann, Polar factorization of maps on Riemannian manifolds, Geom. Funct. Anal. 11 (2001), 589-608.
-
(2001)
Geom. Funct. Anal.
, vol.11
, pp. 589-608
-
-
McCann, R.J.1
-
33
-
-
0003161023
-
Differential geometric aspects of Alexandrov spaces
-
Cambridge Univ. Press, Cambridge, UK
-
Y. Otsu, Differential geometric aspects of Alexandrov spaces, in Comparison Geometry, MSRI Publ. 30 (1997), 135-148, Cambridge Univ. Press, Cambridge, UK.
-
(1997)
Comparison Geometry, MSRI Publ
, vol.30
, pp. 135-148
-
-
Otsu, Y.1
-
34
-
-
84972500357
-
The Riemannian structure of Alexandrov spaces
-
Y. Otsu and T. Shioya, The Riemannian structure of Alexandrov spaces, J. Diff. Geom. 39 (1994), 629-658.
-
(1994)
J. Diff. Geom.
, vol.39
, pp. 629-658
-
-
Otsu, Y.1
Shioya, T.2
-
35
-
-
0001560970
-
The geometry of dissipative evolution equations: the porous medium equation
-
F. Otto, The geometry of dissipative evolution equations: the porous medium equation, Comm. Partial Diff. Eq. 26 (2001), 101-174.
-
(2001)
Comm. Partial Diff. Eq.
, vol.26
, pp. 101-174
-
-
Otto, F.1
-
36
-
-
0001559554
-
Generalization of an inequality by Talagrand, and links with the logarithmic Sobolev inequality
-
F. Otto and C. Villani, Generalization of an inequality by Talagrand, and links with the logarithmic Sobolev inequality, J. Funct. Anal. 173 (2000), 361-400.
-
(2000)
J. Funct. Anal.
, vol.173
, pp. 361-400
-
-
Otto, F.1
Villani, C.2
-
39
-
-
0031285629
-
Estimates for weighted volumes and applications
-
Z. Qian, Estimates for weighted volumes and applications, Quart. J. Math. Oxford 48 (1997), 235-242.
-
(1997)
Quart. J. Math. Oxford
, vol.48
, pp. 235-242
-
-
Qian, Z.1
-
40
-
-
20744448674
-
Transport inequalities, gradient estimates, entropy, and Ricci curvature
-
M.-K. von Renesse and K.-T. Sturm, Transport inequalities, gradient estimates, entropy, and Ricci curvature, Comm. Pure Appl. Math. 58 (2005), 923-940.
-
(2005)
Comm. Pure Appl. Math.
, vol.58
, pp. 923-940
-
-
von Renesse, M.-K.1
Sturm, K.-T.2
-
41
-
-
12944272538
-
Convex functionals of probability measures and nonlinear diffusions on manifolds
-
K.-T. Sturm, Convex functionals of probability measures and nonlinear diffusions on manifolds, J. Math. Pures. Appl. 84 (2005), 149-168.
-
(2005)
J. Math. Pures. Appl.
, vol.84
, pp. 149-168
-
-
Sturm, K.-T.1
-
42
-
-
33750193237
-
On the geometry of metric measure spaces
-
K.-T. Sturm, On the geometry of metric measure spaces, Acta Math. 196 (2006), 65-131.
-
(2006)
Acta Math
, vol.196
, pp. 65-131
-
-
Sturm, K.-T.1
-
43
-
-
0039849447
-
An inequality for a functional of probability distributions and its application to Kac's one-dimensional model of a Maxwellian gas
-
H. Tanaka, An inequality for a functional of probability distributions and its application to Kac's one-dimensional model of a Maxwellian gas, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 27 (1973), 47-52.
-
(1973)
Z. Wahrscheinlichkeitstheorie und Verw. Gebiete
, vol.27
, pp. 47-52
-
-
Tanaka, H.1
-
44
-
-
1542342359
-
Topics in Optimal Transportation
-
Amer. Math. Soc., Providence, RI
-
C. Villani, Topics in Optimal Transportation, Graduate Studies in Mathematics 58, Amer. Math. Soc., Providence, RI, 2003.
-
(2003)
Graduate Studies in Mathematics
, vol.58
-
-
Villani, C.1
-
45
-
-
0007291681
-
Markov processes over denumerable products of spaces describing large systems of automata
-
L. Wasserstein, Markov processes over denumerable products of spaces describing large systems of automata, Problems of Information Transmission 5 (1969), 47-82.
-
(1969)
Problems of Information Transmission
, vol.5
, pp. 47-82
-
-
Wasserstein, L.1
-
46
-
-
0003252368
-
Ergodic Theory and Semisimple Groups
-
Birkhäuser, Basel
-
R. Zimmer, Ergodic Theory and Semisimple Groups, Monographs in Mathematics 81 (1984), Birkhäuser, Basel.
-
(1984)
Monographs in Mathematics
, vol.81
-
-
Zimmer, R.1
|