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Volumn 211, Issue 993, 2011, Pages 1-83

Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems

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EID: 84860541260     PISSN: 00659266     EISSN: 19476221     Source Type: Journal    
DOI: 10.1090/S0065-9266-2010-00610-0     Document Type: Article
Times cited : (34)

References (45)
  • 1
    • 2442517322 scopus 로고    scopus 로고
    • Geometric inequalities via a general comparison principle for interacting gases
    • DOI 10.1007/s00039-004-0455-x
    • M. Agueh, N. Ghoussoub, and X. Kang, Geometric inequalities via a general comparison principle for interacting gases, Geom. Funct. Anal. 14(2004), no. 1, 215-244. MR2053603 (2005c:82050) (Pubitemid 38640649)
    • (2004) Geometric and Functional Analysis , vol.14 , Issue.1 , pp. 215-244
    • Agueh, M.1    Ghoussoub, N.2    Kang, X.3
  • 2
    • 0141682220 scopus 로고    scopus 로고
    • Comportement asymptotique des équations paraboliques doublement dégénérées
    • DOI 10.1016/S1631-073X(03)00352-2
    • Martial Agueh, Asymptotic behavior for doubly degenerate parabolic equations, C. R. Math. Acad. Sci. Paris 337(2003), no. 5, 331-336. MR2016985 (2004i:35194) (Pubitemid 37223490)
    • (2003) Comptes Rendus Mathematique , vol.337 , Issue.5 , pp. 331-336
    • Agueh, M.1
  • 3
    • 37649010339 scopus 로고    scopus 로고
    • Hamiltonian ODEs in the Wasserstein space of probability measures
    • MR2361303 2009b:37101
    • Luigi Ambrosio and Wilfred Gangbo, Hamiltonian ODEs in the Wasserstein space of probability measures, Comm. Pure Appl. Math. 61(2008), no. 1, 18-53. MR2361303 (2009b:37101)
    • (2008) Comm. Pure Appl. Math. , vol.61 , Issue.1 , pp. 18-53
    • Ambrosio, L.1    Gangbo, W.2
  • 4
    • 78650383933 scopus 로고    scopus 로고
    • Construction of the parallel transport in the Wasserstein space
    • MR2482206
    • Luigi Ambrosio and Nicola Gigli, Construction of the parallel transport in the Wasserstein space, Methods Appl. Anal. 15(2008), 1-29. MR2482206
    • (2008) Methods Appl. Anal. , vol.15 , pp. 1-29
    • Ambrosio, L.1    Gigli, N.2
  • 5
    • 33746157912 scopus 로고    scopus 로고
    • Gradient flows in metric spaces and in the space of probability measures
    • Birkhäuser Verlag, Basel, MR2129498 2006k:49001
    • Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré, Gradient flows in metric spaces and in the space of probability measures, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 2005. MR2129498 (2006k:49001)
    • (2005) Lectures in Mathematics ETH Zürich
    • Ambrosio, L.1    Gigli, N.2    Savaré, G.3
  • 6
    • 1642616214 scopus 로고
    • The non-finite homotopy type of some diffeomorphism groups
    • MR0292106 45:1193
    • P. L. Antonelli, D. Burghelea, and P. J. Kahn, The non-finite homotopy type of some diffeomorphism groups, Topology 11(1972), 1-49. MR0292106 (45:1193)
    • (1972) Topology , vol.11 , pp. 1-49
    • Antonelli, P.L.1    Burghelea, D.2    Kahn, P.J.3
  • 7
    • 0001356905 scopus 로고
    • Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits
    • no. fasc, MR0202082 34:1956
    • V. Arnold, Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits, Ann. Inst. Fourier (Grenoble) 16(1966), no. fasc. 1, 319-361. MR0202082 (34:1956)
    • (1966) Ann. Inst. Fourier (Grenoble) , vol.16 , Issue.1 , pp. 319-361
    • Arnold, V.1
  • 8
    • 24244479739 scopus 로고
    • Gauge-independent canonical formulation of relativistic plasma theory
    • MR774764 86b:76055
    • Iwo Białynicki-Birula, John C. Hubbard, and Łukasz A. Turski, Gauge-independent canonical formulation of relativistic plasma theory, Phys. A 128(1984), no. 3, 509-519. MR774764 (86b:76055)
    • (1984) Phys. A , vol.128 , Issue.3 , pp. 509-519
    • Białynicki-Birula, I.1    Hubbard, J.C.2    Turski, Ł.A.3
  • 9
    • 0000200523 scopus 로고
    • On the quantum theory of the electromagnetic field
    • M. Born, On the quantum theory of the electromagnetic field, Proceedings of the Royal Society of London. Series A 143(1934), no. 849, 410-437.
    • (1934) Proceedings of the Royal Society of London. Series A , vol.143 , Issue.849 , pp. 410-437
    • Born, M.1
  • 12
    • 0037821662 scopus 로고    scopus 로고
    • Constrained steepest descent in the 2-Wasserstein metric
    • E. A. Carlen and W. Gangbo, Constrained steepest descent in the 2-Wasserstein metric, Ann. of Math. (2) 157(2003), no. 3, 807-846. MR1983782 (2004c:49027) (Pubitemid 36803088)
    • (2003) Annals of Mathematics , vol.157 , Issue.3 , pp. 807-846
    • Carlen, E.A.1    Gangbo, W.2
  • 13
    • 32544445429 scopus 로고    scopus 로고
    • Contractions in the 2-Wasserstein length space and thermalization of granular media
    • DOI 10.1007/s00205-005-0386-1
    • Jose A. Carrillo, Robert J. McCann, and Cedric Villani, Contractions in the 2-Wasserstein length space and thermalization of granular media, Arch. Ration. Mech. Anal. 179(2006), no. 2, 217-263. MR2209130 (2006j:76121) (Pubitemid 43237778)
    • (2006) Archive for Rational Mechanics and Analysis , vol.179 , Issue.2 , pp. 217-263
    • Carrillo, J.A.1    McCann, R.J.2    Villani, C.3
  • 14
    • 0032367156 scopus 로고    scopus 로고
    • The Maxwell-Vlasov equations in Euler-Poincaré form
    • MR1623546 99e:76131
    • Hernan Cendra, Darryl D. Holm, Mark J. W. Hoyle, and Jerrold E. Marsden, The Maxwell-Vlasov equations in Euler-Poincaré form, J. Math. Phys. 39(1998), no. 6, 3138-3157. MR1623546 (99e:76131)
    • (1998) J. Math. Phys. , vol.39 , Issue.6 , pp. 3138-3157
    • Cendra, H.1    Holm, D.D.2    Hoyle, M.J.W.3    Marsden, J.E.4
  • 15
    • 0003313133 scopus 로고
    • Properties of infinite dimensional Hamiltonian systems
    • Springer-Verlag, Berlin, MR0650113 58:31218
    • Paul R. Chernoff and Jerrold E. Marsden, Properties of infinite dimensional Hamiltonian systems, Lecture Notes in Mathematics, Vol. 425, Springer-Verlag, Berlin, 1974. MR0650113 (58:31218)
    • (1974) Lecture Notes in Mathematics , vol.425
    • Chernoff, P.R.1    Marsden, J.E.2
  • 16
    • 1242299735 scopus 로고    scopus 로고
    • A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities
    • DOI 10.1016/S0001-8708(03)00080-X
    • D. Cordero-Erausquin, B. Nazaret, and C. Villani, A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities, Adv. Math. 182(2004), no. 2, 307-332. MR2032031 (2005b:26023) (Pubitemid 38236234)
    • (2004) Advances in Mathematics , vol.182 , Issue.2 , pp. 307-332
    • Cordero-Erausquin, D.1    Nazaret, B.2    Villani, C.3
  • 18
    • 0001052255 scopus 로고
    • Groups of diffeomorphisms and the notion of an incompressible fluid
    • MR0271984 42:6865
    • David G. Ebin and Jerrold Marsden, Groups of diffeomorphisms and the notion of an incompressible fluid., Ann. of Math. (2) 92(1970), 102-163. MR0271984 (42:6865)
    • (1970) Ann. of Math. , vol.92 , Issue.2 , pp. 102-163
    • Ebin, D.G.1    Marsden, J.2
  • 19
    • 0001103156 scopus 로고    scopus 로고
    • The geometry of optimal transportation
    • Wilfrid Gangbo and Robert J. McCann, The geometry of optimal transportation, Acta Math. 177(1996), no. 2, 113-161. MR1440931 (98e:49102) (Pubitemid 126345872)
    • (1996) Acta Mathematica , vol.177 , Issue.2 , pp. 113-161
    • Gangbo, W.1    McCann, R.J.2
  • 20
    • 77049089463 scopus 로고    scopus 로고
    • Lagrangian dynamics on an infinite-dimensional torus; a weak KAM theorem
    • Wilfrid Gangbo and Adrian Tudorascu, Lagrangian dynamics on an infinite-dimensional torus; a weak KAM theorem, Adv. Math. 224(2010), no. 1, 260-292.
    • (2010) Adv. Math. , vol.224 , Issue.1 , pp. 260-292
    • Gangbo, W.1    Tudorascu, A.2
  • 21
    • 0004194874 scopus 로고
    • Prentice-Hall Inc., Englewood Cliffs, N. J., MR0348781 50:1276
    • Victor Guillemin and Alan Pollack, Differential topology, Prentice-Hall Inc., Englewood Cliffs, N. J., 1974. MR0348781 (50:1276)
    • (1974) Differential Topology
    • Guillemin, V.1    Pollack, A.2
  • 22
    • 84966236065 scopus 로고
    • The inverse function theorem of Nash and Moser
    • MR656198 83j:58014
    • Richard S. Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. (N. S.) 7(1982), no. 1, 65-222. MR656198 (83j:58014)
    • (1982) Bull. Amer. Math. Soc. (N. S.) , vol.7 , Issue.1 , pp. 65-222
    • Hamilton, R.S.1
  • 23
    • 0032343437 scopus 로고    scopus 로고
    • The variational formulation of the Fokker-Planck equation
    • electronic, MR1617171 2000b:35258
    • Richard Jordan, David Kinderlehrer, and Felix Otto, The variational formulation of the Fokker-Planck equation, SIAM J. Math. Anal. 29(1998), no. 1, 1-17 (electronic). MR1617171 (2000b:35258)
    • (1998) SIAM J. Math. Anal. , vol.29 , Issue.1 , pp. 1-17
    • Jordan, R.1    Kinderlehrer, D.2    Otto, F.3
  • 24
    • 47049111063 scopus 로고    scopus 로고
    • Poisson geometry and first integrals of geostrophic equations
    • MR2449883
    • Boris Khesin and Paul Lee, Poisson geometry and first integrals of geostrophic equations, Phys. D 237(2008), no. 14-17, 2072-2077. MR2449883
    • (2008) Phys. D. , vol.237 , Issue.14-17 , pp. 2072-2077
    • Khesin, B.1    Lee, P.2
  • 25
    • 0004341311 scopus 로고    scopus 로고
    • Interscience Publishers, a division of John Wiley & Sons, New York-London, 1963, MR0152974 27:2945
    • Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol I, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1963. MR0152974 (27:2945)
    • Foundations of Differential Geometry , vol.1
    • Kobayashi, S.1    Nomizu, K.2
  • 27
    • 36649022948 scopus 로고    scopus 로고
    • Some geometric calculations on Wasserstein space
    • MR2358290 2009b:58014
    • John Lott, Some geometric calculations on Wasserstein space, Comm. Math. Phys. 277(2008), no. 2, 423-437. MR2358290 (2009b:58014)
    • (2008) Comm. Math. Phys. , vol.277 , Issue.2 , pp. 423-437
    • Lott, J.1
  • 28
    • 62049083002 scopus 로고    scopus 로고
    • Ricci curvature for metric-measure spaces via optimal transport
    • MR2480619
    • John Lott and Cédric Villani, Ricci curvature for metric-measure spaces via optimal transport, Ann. of Math. (2) 169(2009), 903-991. MR2480619
    • (2009) Ann. of Math. , vol.169 , Issue.2 , pp. 903-991
    • Lott, J.1    Villani, C.2
  • 29
    • 23744458381 scopus 로고    scopus 로고
    • Balls have the worst best Sobolev inequalities
    • Francesco Maggi and Cédric Villani, Balls have the worst best Sobolev inequalities, J. Geom. Anal. 15(2005), no. 1, 83-121. MR2132267 (2006a:26041) (Pubitemid 41121682)
    • (2005) Journal of Geometric Analysis , vol.15 , Issue.1 , pp. 83-121
    • Maggi, F.1    Villani, C.2
  • 31
    • 0003274786 scopus 로고    scopus 로고
    • Introduction to mechanics and symmetry
    • second ed., Springer-Verlag, New York, MR1723696 2000i:70002
    • Jerrold E. Marsden and Tudor S. Ratiu, Introduction to mechanics and symmetry, second ed., Texts in Applied Mathematics, vol. 17, Springer-Verlag, New York, 1999. MR1723696 (2000i:70002)
    • (1999) Texts in Applied Mathematics , vol.17
    • Marsden, J.E.1    Ratiu, T.S.2
  • 32
    • 49049133333 scopus 로고
    • The Hamiltonian structure of the Maxwell-Vlasov equations
    • MR657741 84b:82037
    • Jerrold E. Marsden and Alan Weinstein, The Hamiltonian structure of the Maxwell-Vlasov equations, Phys. D 4(1981/82), no. 3, 394-406. MR657741 (84b:82037)
    • (1981) Phys. D , vol.4 , Issue.3 , pp. 394-406
    • Marsden, J.E.1    Weinstein, A.2
  • 33
    • 0031161793 scopus 로고    scopus 로고
    • A convexity principle for interacting gases
    • DOI 10.1006/aima.1997.1634, PII S0001870897916340
    • Robert J. McCann, A convexity principle for interacting gases, Adv. Math. 128(1997), no. 1, 153-179. MR1451422 (98e:82003) (Pubitemid 127171227)
    • (1997) Advances in Mathematics , vol.128 , Issue.1 , pp. 153-179
    • McCann, R.J.1
  • 35
    • 0037506180 scopus 로고    scopus 로고
    • Introduction to symplectic topology
    • second ed., The Clarendon Press, Oxford University Press, New York, MR1698616 2000g:53098
    • Dusa McDuff and Dietmar Salamon, Introduction to symplectic topology, second ed., Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1998. MR1698616 (2000g:53098)
    • (1998) Oxford Mathematical Monographs
    • McDuff, D.1    Salamon, D.2
  • 36
    • 0001335921 scopus 로고
    • Remarks on infinite-dimensional Lie groups
    • Les Houches, North-Holland, Amsterdam, MR830252 87g:22024
    • J. Milnor, Remarks on infinite-dimensional Lie groups, Relativity, groups and topology, II (Les Houches, 1983), North-Holland, Amsterdam, 1984, pp. 1007-1057. MR830252 (87g:22024)
    • (1983) Relativity, Groups and Topology, II , pp. 1007-1057
    • Milnor, J.1
  • 37
    • 0008059961 scopus 로고    scopus 로고
    • Infinite-dimensional Lie groups
    • Providence, RI, Translated from the 1979 Japanese original and revised by the author, MR1421572 97k:22029
    • Hideki Omori, Infinite-dimensional Lie groups, Translations of Mathematical Monographs, vol. 158, American Mathematical Society, Providence, RI, 1997, Translated from the 1979 Japanese original and revised by the author. MR1421572 (97k:22029)
    • (1997) Translations of Mathematical Monographs, Vol. 158, American Mathematical Society
    • Omori, H.1
  • 38
    • 33846815179 scopus 로고    scopus 로고
    • Floer-Novikov cohomology and the flux conjecture
    • MR2276532 2007k:53147
    • K. Ono, Floer-Novikov cohomology and the flux conjecture, Geom. Funct. Anal. 16(2006), no. 5, 981-1020. MR2276532 (2007k:53147)
    • (2006) Geom. Funct. Anal. , vol.16 , Issue.5 , pp. 981-1020
    • Ono, K.1
  • 39
    • 0001560970 scopus 로고    scopus 로고
    • The geometry of dissipative evolution equations: The porous medium equation
    • Felix Otto, The geometry of dissipative evolution equations: the porous medium equation, Comm. Partial Differential Equations 26(2001), no. 1-2, 101-174. MR1842429 (2002j:35180) (Pubitemid 33731270)
    • (2001) Communications in Partial Differential Equations , vol.26 , Issue.1-2 , pp. 101-174
    • Otto, F.1
  • 40
    • 0004323587 scopus 로고
    • Springer-Verlag, Berlin, Translated from the German by P. Achuthan and K. Venkatesan, With an introduction by Charles P. Enz, MR636099 83b:81003
    • Wolfgang Pauli, General principles of quantum mechanics, Springer-Verlag, Berlin, 1980, Translated from the German by P. Achuthan and K. Venkatesan, With an introduction by Charles P. Enz. MR636099 (83b:81003)
    • (1980) General Principles of Quantum Mechanics
    • Pauli, W.1
  • 41
    • 0004057553 scopus 로고
    • Functional analysis
    • second ed., McGraw-Hill Inc., New York, MR1157815 92k:46001
    • Walter Rudin, Functional analysis, second ed., International Series in Pure and Applied Mathematics, McGraw-Hill Inc., New York, 1991. MR1157815 (92k:46001)
    • (1991) International Series in Pure and Applied Mathematics
    • Rudin, W.1
  • 42
    • 33750180350 scopus 로고    scopus 로고
    • On the geometry of metric measure spaces. I
    • MR2237206 2007k:53051a
    • Karl-Theodor Sturm, On the geometry of metric measure spaces. I, Acta Math. 196(2006), no. 1, 65-131. MR2237206 (2007k:53051a)
    • (2006) Acta Math. , vol.196 , Issue.1 , pp. 65-131
    • Sturm, K.1
  • 43
    • 33750180350 scopus 로고    scopus 로고
    • On the geometry of metric measure spaces. II
    • DOI 10.1007/s11511-006-0003-7
    • -, On the geometry of metric measure spaces. II, Acta Math. 196(2006), no. 1, 133-177. MR2237207 (2007k:53051b) (Pubitemid 44598870)
    • (2006) Acta Mathematica , vol.196 , Issue.1 , pp. 133-177
    • Sturm, K.-T.1
  • 45
    • 0000595516 scopus 로고
    • Symplectic manifolds and their Lagrangian submanifolds
    • 1971, MR0286137 44:3351
    • Alan Weinstein, Symplectic manifolds and their Lagrangian submanifolds, Advances in Math. 6(1971), 329-346 (1971). MR0286137 (44:3351)
    • (1971) Advances in Math. , vol.6 , pp. 329-346
    • Weinstein, A.1


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