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Volumn 3, Issue 1, 2014, Pages 119-139

Ricci curvature on polyhedral surfaces via optimal transportation

Author keywords

Discrete curvature; Discrete Laplacian; Graph theory; Optimal transportation; Tiling

Indexed keywords


EID: 84933049130     PISSN: None     EISSN: 20751680     Source Type: Journal    
DOI: 10.3390/axioms3010119     Document Type: Article
Times cited : (49)

References (24)
  • 1
    • 31244437181 scopus 로고    scopus 로고
    • Combinatorial curvature for planar graphs
    • Higuchi, Y. Combinatorial curvature for planar graphs. J. Graph Theory 2001, 38, 220-229
    • (2001) J. Graph Theory , vol.38 , pp. 220-229
    • Higuchi, Y.1
  • 2
    • 84880808842 scopus 로고    scopus 로고
    • Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator
    • Bauer, F.; Jost, J.; Liu, S. Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator. Math. Res. Lett. 2012, 19, 1185-1205
    • (2012) Math. Res. Lett , vol.19 , pp. 1185-1205
    • Bauer, F.1    Jost, J.2    Liu, S.3
  • 3
    • 77952021519 scopus 로고    scopus 로고
    • Ricci curvature and eigenvalue estimate on locally finite graphs
    • Lin, Y.; Yau, S.T. Ricci curvature and eigenvalue estimate on locally finite graphs. Math. Res. Lett. 2010, 17, 343-356
    • (2010) Math. Res. Lett , vol.17 , pp. 343-356
    • Lin, Y.1    Yau, S.T.2
  • 4
    • 34247540692 scopus 로고    scopus 로고
    • Geometry and Computing; Springer-Verlag: Berlin, Germany
    • Morvan, J.M. Generalized Curvatures; Geometry and Computing; Springer-Verlag: Berlin, Germany, 2008; Volume 2, xii+266
    • (2008) Generalized Curvatures , vol.2
    • Morvan, J.M.1
  • 5
    • 0003195390 scopus 로고
    • Hyperbolic groups
    • Springer: New York NY, USA
    • Gromov, M. Hyperbolic groups. In Essays in Group Theory; Springer: New York, NY, USA, 1987; pp. 75-263
    • (1987) Essays in Group Theory , pp. 75-263
    • Gromov, M.1
  • 7
    • 84972539061 scopus 로고
    • A combinatorial analogue of a theorem of Myers
    • Stone, D.A. A combinatorial analogue of a theorem of Myers. Ill. J. Math. 1976, 20, 12-21
    • (1976) Ill. J. Math , vol.20 , pp. 12-21
    • Stone, D.A.1
  • 8
    • 84972513486 scopus 로고
    • Correction to my paper: "A combinatorial analogue of a theorem of Myers" ( J. Math. 20 1976, 12-21). Ill
    • Stone, D.A. Correction to my paper: "A combinatorial analogue of a theorem of Myers" (Ill. J. Math. 20 1976, 12-21). Ill. J. Math. 1976, 20, 551-554
    • (1976) J. Math , vol.20 , pp. 551-554
    • Stone, D.A.1
  • 9
    • 0037972746 scopus 로고    scopus 로고
    • Bochner's Method for Cell Complexes and Combinatorial Ricci Curvature
    • Forman, R. Bochner's Method for Cell Complexes and Combinatorial Ricci Curvature. Discret. Comput. Geom. 2003, 29, 323-374
    • (2003) Discret. Comput. Geom , vol.29 , pp. 323-374
    • Forman, R.1
  • 10
    • 62049085614 scopus 로고    scopus 로고
    • Mass transportation and rough curvature bounds for discrete spaces
    • Bonciocat, A.I.; Sturm, K.T. Mass transportation and rough curvature bounds for discrete spaces. J. Funct. Anal. 2009, 256, 2944-2966
    • (2009) J. Funct. Anal , vol.256 , pp. 2944-2966
    • Bonciocat, A.I.1    Sturm, K.T.2
  • 11
    • 84893874148 scopus 로고    scopus 로고
    • Ollivier's Ricci curvature, local clustering and curvature dimension inequalities on graphs
    • Jost, J.; Liu, S. Ollivier's Ricci curvature, local clustering and curvature dimension inequalities on graphs. Discret. Comput. Geom. 2014, 51, 300-322
    • (2014) Discret. Comput. Geom , vol.51 , pp. 300-322
    • Jost, J.1    Liu, S.2
  • 12
    • 58149087855 scopus 로고    scopus 로고
    • Ricci curvature of Markov chains on metric spaces
    • Ollivier, Y. Ricci curvature of Markov chains on metric spaces. J. Funct. Anal. 2009, 256, 810-864
    • (2009) J. Funct. Anal , vol.256 , pp. 810-864
    • Ollivier, Y.1
  • 13
    • 84872351240 scopus 로고    scopus 로고
    • A survey of Ricci curvature for metric spaces and Markov chains
    • Mathematical Society of Japan: Tokyo Japan
    • Ollivier, Y. A survey of Ricci curvature for metric spaces and Markov chains. In Probabilistic Approach to Geometry; Mathematical Society of Japan: Tokyo, Japan, 2010; pp. 343-381
    • (2010) Probabilistic Approach to Geometry , pp. 343-381
    • Ollivier, Y.1
  • 15
    • 0004267646 scopus 로고    scopus 로고
    • Princeton Landmarks in Mathematics, Princeton University Press: Princeton, NJ, USA
    • Rockafellar, R.T. Convex Analysis; Princeton Landmarks in Mathematics, Princeton University Press: Princeton, NJ, USA, 1997
    • (1997) Convex Analysis
    • Rockafellar, R.T.1
  • 16
    • 0003781238 scopus 로고    scopus 로고
    • Cambridge University Press: Cambridge, UK
    • Norris, J.R. Markov Chains; Cambridge University Press: Cambridge, UK, 1998
    • (1998) Markov Chains
    • Norris, J.R.1
  • 20
    • 85054237574 scopus 로고    scopus 로고
    • (accessed on 6 March 2014)
    • Sage computer program. Available online: http://www.sagemath.org (accessed on 6 March 2014)
  • 21
  • 22
    • 36549070221 scopus 로고    scopus 로고
    • A discrete Laplace-Beltrami operator for simplicial surfaces
    • Bobenko, A.I.; Springborn, B.A. A discrete Laplace-Beltrami operator for simplicial surfaces. Discret. Comput. Geom. 2007, 38, 740-756
    • (2007) Discret. Comput. Geom , vol.38 , pp. 740-756
    • Bobenko, A.I.1    Springborn, B.A.2
  • 24
    • 80051905996 scopus 로고    scopus 로고
    • Discrete Laplacians on general polygonal meshes
    • Alexa, M.;Wardetzky, M. Discrete Laplacians on general polygonal meshes. ACM Trans. Graph. (TOG) 2011, 30, 102
    • (2011) ACM Trans. Graph. (TOG) , vol.30 , pp. 102
    • Alexa, M.1    Wardetzky, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.