메뉴 건너뛰기




Volumn 55, Issue 4, 2012, Pages 723-735

First variation formula in wasserstein spaces over compact alexandrov spaces

Author keywords

Alexandrov spaces; First variation formula; Gradient flow; Wasserstein spaces

Indexed keywords


EID: 84871778243     PISSN: 00084395     EISSN: None     Source Type: Journal    
DOI: 10.4153/CMB-2011-110-3     Document Type: Article
Times cited : (16)

References (21)
  • 2
    • 0003365247 scopus 로고    scopus 로고
    • A course in metric geometry
    • American Mathematical Society, Providence, RI
    • D. Burago, Y. Burago, and S. Ivanov, A course in metric geometry. Graduate Studies in Mathematics, 33, American Mathematical Society, Providence, RI, 2001.
    • (2001) Graduate Studies in Mathematics , vol.33
    • Burago, D.1    Burago, Y.2    Ivanov, S.3
  • 3
    • 0001787207 scopus 로고
    • A. D. Alexandrov spaces with curvatures bounded below (Russian)
    • (284), 222
    • Y. Burago, M. Gromov, and G. Perel'man, A. D. Alexandrov spaces with curvatures bounded below (Russian). Uspekhi Mat. Nauk 47(1992), no. 2(284), 3-51, 222;
    • (1992) Uspekhi Mat. Nauk , vol.47 , Issue.2 , pp. 3-51
    • Burago, Y.1    Gromov, M.2    Perel'Man, G.3
  • 4
    • 84871748571 scopus 로고
    • English translation in Russian Math
    • English translation in Russian Math. Surveys 47(1992), no. 2, 1-58.
    • (1992) Surveys , vol.47 , Issue.2 , pp. 1-58
  • 6
    • 0032343437 scopus 로고    scopus 로고
    • 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), no. 1, 1-17. http://dx.doi.org/10.1137/S0036141096303359
    • (1998) SIAM J. Math. Anal. , vol.29 , Issue.1 , pp. 1-17
    • Jordan, R.1    Kinderlehrer, D.2    Otto, F.3
  • 7
    • 0035639753 scopus 로고    scopus 로고
    • Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces
    • K. Kuwae, Y. Machigashira, and T. Shioya, Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces. Math. Z. 238(2001), no. 2, 269-316. http://dx.doi.org/10.1007/s002090100252
    • (2001) Math. Z. , vol.238 , Issue.2 , pp. 269-316
    • Kuwae, K.1    MacHigashira, Y.2    Shioya, T.3
  • 8
    • 62049083002 scopus 로고    scopus 로고
    • Ricci curvature for metric-measure spaces via optimal transport
    • J. Lott and C. Villani, Ricci curvature for metric-measure spaces via optimal transport. Ann. of Math. 169(2009), no. 3, 903-991. http://dx.doi.org/ 10.4007/annals.2009.169.903
    • (2009) Ann. of Math. , vol.169 , Issue.3 , pp. 903-991
    • Lott, J.1    Villani, C.2
  • 9
    • 85009813191 scopus 로고    scopus 로고
    • Open map theorem for metric spaces
    • A. Lytchak, Open map theorem for metric spaces. St. Petersburg Math. J. 17(2006), no. 3, 477-491.
    • (2006) St. Petersburg Math. J. , vol.17 , Issue.3 , pp. 477-491
    • Lytchak, A.1
  • 10
    • 0035618489 scopus 로고    scopus 로고
    • Polar factorization of maps on Riemannian manifolds
    • R. J. McCann, Polar factorization of maps on Riemannian manifolds. Geom. Funct. Anal. 11(2001), no. 3, 589-608. http://dx.doi.org/10.1007/PL00001679
    • (2001) Geom. Funct. Anal. , vol.11 , Issue.3 , pp. 589-608
    • McCann, R.J.1
  • 11
    • 77954633560 scopus 로고    scopus 로고
    • Ricci flow, entropy and optimal transportation
    • R. J. McCann and P. Topping, Ricci flow, entropy and optimal transportation. Amer. J. Math. 132(2010), no. 3, 711-730. http://dx.doi.org/10. 1353/ajm.0.0110
    • (2010) Amer. J. Math. , vol.132 , Issue.3 , pp. 711-730
    • McCann, R.J.1    Topping, P.2
  • 12
    • 68149156285 scopus 로고    scopus 로고
    • Gradient flows on Wasserstein spaces over compact Alexandrov spaces
    • S. Ohta, Gradient flows on Wasserstein spaces over compact Alexandrov spaces. Amer. J. Math. 131(2009), no. 2, 475-516. http://dx.doi.org/10.1353/ajm. 0.0048
    • (2009) Amer. J. Math. , vol.131 , Issue.2 , pp. 475-516
    • Ohta, S.1
  • 13
    • 68049121962 scopus 로고    scopus 로고
    • Heat flow on Finsler manifolds
    • S. Ohta and K.-T. Sturm, Heat flow on Finsler manifolds. Comm. Pure Appl. Math. 62(2009), no. 10, 1386-1433. http://dx.doi.org/10.1002/cpa.20273
    • (2009) Comm. Pure Appl. Math. , vol.62 , Issue.10 , pp. 1386-1433
    • Ohta, S.1    Sturm, K.-T.2
  • 14
    • 84972500357 scopus 로고
    • The Riemannian structure of Alexandrov spaces
    • Y. Otsu and T. Shioya, The Riemannian structure of Alexandrov spaces. J. Differential Geom. 39(1994), no. 3, 629-658.
    • (1994) J. Differential Geom. , vol.39 , Issue.3 , pp. 629-658
    • Otsu, Y.1    Shioya, T.2
  • 15
    • 0001560970 scopus 로고    scopus 로고
    • The geometry of dissipative evolution equations: The porous medium equation
    • F. Otto, The geometry of dissipative evolution equations: the porous medium equation. Comm. Partial Differential Equations 26(2001), no. 1-2, 101-174. http://dx.doi.org/10.1081/PDE-100002243 (Pubitemid 33731270)
    • (2001) Communications in Partial Differential Equations , vol.26 , Issue.1-2 , pp. 101-174
    • Otto, F.1
  • 17
    • 20744448674 scopus 로고    scopus 로고
    • Transport inequalities, gradient estimates, entropy, and Ricci curvature
    • DOI 10.1002/cpa.20060
    • M.-K. von Renesse and K.-T. Sturm, Transport inequalities, gradient estimates, entropy, and Ricci curvature. Comm. Pure Appl.Math. 58(2005), no. 7, 923-940. http://dx.doi.org/10.1002/cpa.20060 (Pubitemid 40855324)
    • (2005) Communications on Pure and Applied Mathematics , vol.58 , Issue.7 , pp. 923-940
    • Von Renesse, M.-K.1    Sturm, K.-T.2
  • 18
    • 34547422503 scopus 로고    scopus 로고
    • Gradient flows and diffusion semigroups in metric spaces under lower curvature bounds
    • G. Savaŕe, Gradient flows and diffusion semigroups in metric spaces under lower curvature bounds. C. R. Math. Acad. Sci. Paris 345(2007), no. 3, 151-154.
    • (2007) C. R. Math. Acad. Sci. Paris , vol.345 , Issue.3 , pp. 151-154
    • Savaŕe, G.1
  • 19
    • 12944272538 scopus 로고    scopus 로고
    • Convex functionals of probability measures and nonlinear diffusions on manifolds
    • DOI 10.1016/j.matpur.2004.11.002, PII S0021782404001485
    • K.-T. Sturm, Convex functionals of probability measures and nonlinear diffusions on manifolds. J. Math. Pures Appl. 84(2005), no. 2, 149-168. http://dx.doi.org/10.1016/j.matpur.2004.11.002 (Pubitemid 40190039)
    • (2005) Journal des Mathematiques Pures et Appliquees , vol.84 , Issue.2 , pp. 149-168
    • Sturm, K.-T.1
  • 20
    • 33750180350 scopus 로고    scopus 로고
    • On the geometry of metric measure spaces. I
    • -, On the geometry of metric measure spaces. I. Acta Math. 196(2006), no. 1, 65-131. http://dx.doi.org/10.1007/s11511-006-0002-8
    • (2006) Acta Math. , vol.196 , Issue.1 , pp. 65-131
    • Sturm, K.-T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.