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Volumn 84, Issue 2, 2005, Pages 149-168

Convex functionals of probability measures and nonlinear diffusions on manifolds

Author keywords

Bakry Emery criterion; Entropy; Fast diffusion; Gradient flow; Nonlinear diffusion; Porous medium equation; Ricci curvature; Wasserstein distance

Indexed keywords


EID: 12944272538     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2004.11.002     Document Type: Article
Times cited : (83)

References (14)
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    • D. Bakry M. Emery Hypercontractivité de semi-groupes de diffusion C. R. Acad. Sci. Paris Sér. I 299 1984 775-778
    • (1984) C. R. Acad. Sci. Paris Sér. I , vol.299 , pp. 775-778
    • Bakry, D.1    Emery, M.2
  • 2
    • 0004112521 scopus 로고
    • Cambridge Tracts in Math. Cambridge, UK: Cambridge Univ. Press
    • I. Chavel Riemannian Geometry: A Modern Introduction Cambridge Tracts in Math. vol. 108 1993 Cambridge Univ. Press Cambridge, UK
    • (1993) Riemannian Geometry: A Modern Introduction , vol.108
    • Chavel, I.1
  • 3
    • 0035602628 scopus 로고    scopus 로고
    • A Riemannian interpolation inequality à la Borell, Brascamb and Lieb
    • D. Cordero-Erausquin R. McCann M. Schmuckenschläger A Riemannian interpolation inequality à la Borell, Brascamb 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
  • 7
    • 13244275799 scopus 로고    scopus 로고
    • Private communication
    • A. Lytchak Private communication 2003
    • (2003)
    • Lytchak, A.1
  • 8
    • 0035618489 scopus 로고    scopus 로고
    • Polar factorization of maps on Riemannian manifolds
    • R. 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.1
  • 9
    • 0001560970 scopus 로고    scopus 로고
    • The geometry of dissipative evolution equation: The porous medium equation
    • F. Otto The geometry of dissipative evolution equation: The porous medium equation Comm. Partial Differential Equations 26 2001 101-174
    • (2001) Comm. Partial Differential Equations , vol.26 , pp. 101-174
    • Otto, F.1
  • 10
    • 0001559554 scopus 로고    scopus 로고
    • Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
    • F. Otto 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
  • 11
    • 13244267853 scopus 로고    scopus 로고
    • Perelman, Petrunin, Unpublished manuscript
    • Perelman, Petrunin, Unpublished manuscript
  • 13
    • 12944264224 scopus 로고    scopus 로고
    • Transport inequalities, gradient estimates, entropy and Ricci curvature
    • in press
    • M.-K. von Renesse K.T. Sturm Transport inequalities, gradient estimates, entropy and Ricci curvature Comm. Pure Appl. Math. 2003 in press
    • (2003) Comm. Pure Appl. Math.
    • von Renesse, M.-K.1    Sturm, K.T.2
  • 14


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.