Publications-Liu

Home

Activities

Publications

Talks

Teaching

Research Seminars

Preprints

@ googlescholar

  1. with Supanat Kamtue, Florentin Münch and Norbert Peyerimhoff
    Entropic curvature not comparable to other curvatures -- or is it?
    arXiv:2404.04581

  2. with Supanat Kamtue, Florentin Münch and Norbert Peyerimhoff
    Bakry-Émery calculus for entropic curvature, new diameter estimates, and spectral gaps
    arXiv:2312.09686

  3. with Wenbo Li
    On the nontrivial extremal eigenvalues of graphs
    arXiv:2310.17520

  4. with David Cushing, Supanat Kamtue, Riikka Kangaslampi, Florentin Münch and Norbert Peyerimhoff
    Bakry-Émery and Ollivier Ricci curvature of Cayley graphs
    arXiv:2310.15953

  5. with Chuanyuan Ge and Dong Zhang
    New graph invariants based on p-Laplacians
    arXiv:2310.08189

  6. with Chunyang Hu
    Vertex isoperimetry on signed graphs and spectra of non-bipartite Cayley graphs
    arXiv:2306.05306

  7. with Xueping Huang and Qing Xia
    Bounding the diameter and eigenvalues of amply regular graphs via Lin-Lu-Yau curvature
    arXiv:2210.02988

  8. with Chunyang Hu
    Discrete Bakry-Émery curvature tensors and matrices of connection graphs
    arXiv:2209.10762

  9. with David Cushing, Supanat Kamtue, Florentin Münch, Norbert Peyerimhoff, and Ben Snodgrass.
    Bakry-Émery curvature sharpness and curvature flow in finite weighted graphs. I. Theory
    arXiv:2204.10064

  10. An optimal dimension-free upper bound for eigenvalue ratios
    arXiv:1405.2213

  11. Wei Li, Jiao Gu, Shiping Liu, Yueying Zhu, Shengfeng Deng, Longfeng Zhao, Jihui Han, Xu Cai
    Optimal Transport in Worldwide Metro Networks
    arXiv:1403.7844

Publications

@ MathSciNet @ ORCiD

  1. with Wenbo Li
    Graph bundles and Ricci-flatness
    Bulletin of the London Mathematical Society 56 (2024), no. 2, 523-535. link, arXiv

  2. with Chuanyuan Ge and Dong Zhang
    Nodal domain theorems for p-Laplacians on signed graphs
    Journal of Spectral Theory 13 (2023), no. 3, 937-989. link, arXiv

  3. with David Cushing, Supanat Kamtue, Florentin Münch, Norbert Peyerimhoff, and Ben Snodgrass.
    Bakry-Émery curvature sharpness and curvature flow in finite weighted graphs: Implementation
    Axioms 12 (2023), no. 6, 577 link , arXiv

  4. with Chuanyuan Ge
    Symmetric matrices, signed graphs, and nodal domain theorems
    Calculus of Variations and Partial Differential Equations 62 (2023), Article 137 link , arXiv

  5. with Florentin Münch and Norbert Peyerimhoff
    Rigidity properties of the hypercube via Bakry-Émery curvature
    Mathematische Annalen 388 (2024), no. 2, 1225-1259. link, arXiv

  6. with David Cushing, Supanat Kamtue, and Norbert Peyerimhoff
    Bakry-Émery curvature on graphs as an eigenvalue problem
    Calculus of Variations and Partial Differential Equations 61 (2022), no. 2, Article 62 link , full-tex view-only version, arXiv

  7. with Xintian Li
    Lin-Lu-Yau curvature and diameter of amply regular graphs
    Journal of University of Science and Technology of China (JUSTC) 51 (2021), no.12, 889-893. link arXiv

  8. with David Cushing, Supanat Kamtue, Riikka Kangaslampi and Norbert Peyerimhoff
    Curvature, graph products and Ricci flatness
    Journal of Graph Theory 96 (2021), no. 4, 522-553. link arXiv

  9. with Matthias Keller and Norbert Peyerimhoff
    A note on eigenvalue bounds for non-compact manifolds
    Mathematische Nachrichten 294 (2021), no. 6, 1134-1139. link, arXiv

  10. with David Cushing, Supanat Kamtue, Jack Koolen, Florentin Münch and Norbert Peyerimhoff
    Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature
    Advances in Mathematics 369 (2020), 107188. link arXiv

  11. with Michel Bonnefont, Sylvain Golénia, Matthias Keller and Florentin Münch
    Magnetic sparseness and Schrödinger operators on graphs
    Annales Henri Poincaré 21 (2020), no. 5, 1489-1516. link arXiv

  12. with David Cushing, Riikka Kangaslampi, Valtteri Lipiäinen and George William Stagg
    The Graph Curvature Calculator and the curvatures of cubic graphs
    Experimental Mathematics 31 (2022), no. 2, 583-595 link, arXiv

    Graph Curvature Calculator (If you have found this software useful, please cite the above article.)

  13. with Fatihcan M. Atay
    Cheeger constants, structural balance, and spectral clustering analysis for signed graphs
    Discrete Mathematics 343 (2020), no. 1, 111616 link, arXiv, MPI MiS Preprint 111/2014

    included in the Editors' Choice selections for 2019 link
    The Editors' Choice papers are nominated by the editors, and the journal select 10-15 of the best papers from the year to be featured. These papers will be free to access until 30th March 2021.

  14. with David Cushing, Riikka Kangaslampi, Yong Lin, Linyuan Lu and Shing-Tung Yau
    Erratum for Ricci-flat graphs with girth at least five
    Communications in Analysis and Geometry 29 (2021), no. 8, 1775-1781.     link, arXiv

  15. with David Cushing, Riikka Kangaslampi, Yong Lin, Linyuan Lu and Shing-Tung Yau
    Ricci-flat cubic graphs with girth five
    Communications in Analysis and Geometry 29 (2021), no. 7, 1559-1570.     link, arXiv

  16. with Norbert Peyerimhoff and Alina Vdovina
    Signatures, lifts, and eigenvalues of graphs
    accepted in: Fatihcan Atay, Pavel Kurasov, and Delio Mugnolo (Eds.) Discrete and Continuous Models in the Theory of Networks, Operator Theory: Advances and Applications 281 (2020), Birkhäuser. link arXiv

  17. with David Cushing, Florentin Münch and Norbert Peyerimhoff
    Curvature calculations for antitrees
    in: Matthias Keller, Daniel Lenz, and Radoslaw Wojciechowski (Eds.) Analysis and geometry on graphs and manifolds, London Mahtematical Society Lecture Notes Series 461 (2020), pp. 21-54, Cambridge University Press. link arXiv

  18. with Florentin Münch, Norbert Peyerimhoff and Christian Rose
    Distance bounds for graphs with some negative Bakry-Émery curvature
    Analysis and Geometry in Metric Spaces 7 (2019), no. 1, 1-14 link arXiv

  19. with Michela Egidi, Florentin Münch and Norbert Peyerimhoff
    Ricci curvature and eigenvalue estimates for the magnetic Laplacian on manifolds
    Communications in Analysis and Geometry 29 (2021), no. 5, 1127-1156. link, arXiv

  20. with Florentin Münch and Norbert Peyerimhoff
    Curvature and higher order Buser inequalities for the graph connection Laplacian
    SIAM Journal on Discrete Mathematics 33 (2019), no. 1, 257-305 pdf, link, arXiv, MPIM Preprint 2016-3

  21. Areejit Samal, R.P. Sreejith, Jiao Gu, Shiping Liu, Emil Saucan and Jürgen Jost
    Comparative analysis of two discretizations of Ricci curvature for complex networks
    Scientific Reports 8 (2018), Article number 8650 link, arXiv

    Press release: Meaningful relationships - mathematical insights into the geometry of complex networks, June 07, 2018 Max Planck Society news, IDW news

  22. with David Cushing and Norbert Peyerimhoff
    Bakry-Émery curvature functions of graphs
    Canadian Journal of Mathematics 72 (2020), no. 1, 89-143 link, arXiv

  23. with Florentin Münch and Norbert Peyerimhoff
    Bakry-Émery curvature and diameter bounds on graphs
    Calculus of Variations and Partial Differential Equations 57 (2018), no. 2, Article 67 link, full-text view-only version, arXiv

  24. with David Bourne, David Cushing, Florentin Münch and Norbert Peyerimhoff
    Ollivier-Ricci idleness functions of graphs
    SIAM Journal on Discrete Mathematics 32 (2018), no. 2, 1408-1424 link, arXiv, CVGMT link

  25. with Norbert Peyerimhoff
    Eigenvalue ratios of nonnegatively curved graphs
    Combinatorics, Probability and Computing 27 (2018), no. 5, 829-850 link arXiv

  26. with Bobo Hua and Chao Xia
    Liouville theorems for f-harmonic maps into Hadamard spaces
    Pacific Journal of Mathematics 290 (2017), no. 2, 381-402 link, arXiv

  27. with Carsten Lange, Norbert Peyerimhoff and Olaf Post
    Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians
    Calculus of Variations and Partial Differential Equations 54 (2015), no. 4, 4165-4196 link(open access), arXiv

  28. with Jiao Gu, Jürgen Jost and Peter F. Stadler
    Spectral classes of regular, random, and empirical graphs
    Linear Algebra and its Applications 489 (2016), 30-49 link, arXiv

  29. with Jiao Gu and Bobo Hua
    Spectral distances on graphs
    Discrete Applied Mathematics 190/191 (2015), 56-74 link(open access), arXiv

  30. Multi-way dual Cheeger constants and spectral bounds of graphs
    Advances in Mathematics 268 (2015), 306-338 link(open access), arXiv

  31. with Bobo Hua and Jürgen Jost
    Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature
    Journal für die reine und angewandte Mathematik (Crelles Journal) 700 (2015), 1-36 link , arXiv

  32. with Frank Bauer and Jürgen Jost
    Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator
    Mathematical Research Letters 19 (2012), no. 6, 1185-1205 link , arXiv

  33. with Jürgen Jost
    Ollivier's Ricci curvature, local clustering and curvature-dimension inequalities on graphs
    Discrete & Computational Geometry 51 (2014), no. 2, 300-322 link , arXiv

  34. Gradient estimates for solutions of the heat equation under Ricci flow
    Pacific Journal of Mathematics 243 (2009), no. 1, 165-180 link , ResearchGate

Book Chapter

  1. with Frank Bauer, Bobo Hua, Jürgen Jost and Guofang Wang
    The geometric meaning of curvature. Local and nonlocal aspects of Ricci curvature
    in: Modern Approaches to Discrete Curvature, Laurent Najman and Pascal Romon (Eds.) Lecture Notes in Mathematics 2184 (2017), Springer.

Proceedings

  1. Cheeger constants with signatures and spectral clustering via quotient space metrics
    Mini-Workshop: Discrete p-Laplacians: Spectral Theory and Variational Methods in Mathematics and Computer Science, Oberwolfach Reports, 2015 link

  2. with Frank Bauer, Bobo Hua and Jürgen Jost
    Generalized Ricci curvature and the geometry of graphs
    Actes des rencontres du CIRM 3 (2013), no. 1: Discrete curvature: Theory and applications, 69-78 link

PhD Thesis