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Equivalent properties for CD inequalities on graphs with unbounded Laplacians

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Abstract

The CD inequalities are introduced to imply the gradient estimate of Laplace operator on graphs. This article is based on the unbounded Laplacians, and finally concludes some equivalent properties of the CD(K,1) and CD(K,n).

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References

  1. Chung, F., Spectral Graph Theory, CBMS Regional Congerence Series in Mahtematics, 92, American Mathemeatical Society, Providence, RI,1997.

    Google Scholar 

  2. Hua, B. B. and Lin, Y., Stochastic completeness for graphs with curvature dimension conditions, Adv. Math., 306, 2017, 279–302.

    Article  MathSciNet  MATH  Google Scholar 

  3. Bakery, D., Gentil, I. and Ledoux, M., Analysis and geometry of Markov diffusion operators, Number 348 in Grundlehren der Mathematischen Wissenschaften. Springer, Cham, 2014.

    Book  Google Scholar 

  4. Bauer, F., Horn, P., Lin, Y., Lippner, G., Mangoubi, D. and Yau, S.-T., Li-Yau inequality on graphs, Journal of Differential Geometry, 99, 2015, 359–405.

    Article  MathSciNet  MATH  Google Scholar 

  5. Keller, M. and Lenz, D., Unbounded Laplacians on graphs:basic spectral properties and the heat equation, Mathematical Modelling of Natural Phenomena, 5(4), 2011, 198–224.

    Article  MathSciNet  MATH  Google Scholar 

  6. Keller, M. and Lenz, D., Dirichlet forms and stochastic completeness of graphs and subgraphs, Journal Fur Die Reine Und Angewandte Mathematik, 2012(666), 2012, 1074–1076.

    Article  MATH  Google Scholar 

  7. Horn, P., Lin, Y., Liu, S. and Yau, S.-T., Volume doubling, Poincaré inequality and Guassian heat kernel estimate for nonnegative curvature graphs, preprint.

  8. Lin, Y. and Yau, S.-T., Ricci curvature and eigenvalue estimate on locally finite graphs, Math. Res. Lett., 17(2), 2010, 343–356.

    Article  MathSciNet  MATH  Google Scholar 

  9. Lin, Y. and Liu, S., Equivalent properties of CD inequality on graphs, preprint.

  10. Yau, S.-T. and Schoen, R., Lectures on Differential Geometry, Higher Education Press, Beijing, 2014.

    MATH  Google Scholar 

  11. Gudmundsson, S., An Introduction to Riemann Geometry, Beijing University, Beijing, 2004.

    Google Scholar 

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Authors and Affiliations

  1. School of Information, Renmin University of China, Beijing, 100872, China

    Chao Gong & Yong Lin

Authors
  1. Chao Gong
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  2. Yong Lin
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Correspondence to Chao Gong.

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Gong, C., Lin, Y. Equivalent properties for CD inequalities on graphs with unbounded Laplacians. Chin. Ann. Math. Ser. B 38, 1059–1070 (2017). https://doi.org/10.1007/s11401-017-1022-8

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  • DOI: https://doi.org/10.1007/s11401-017-1022-8

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