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@ googlescholar

  1. 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
    arXiv:1807.02384

  2. with David Cushing, Riikka Kangaslampi, Valtteri Lipiäinen and George William Stagg
    The Graph Curvature Calculator and the curvatures of cubic graphs
    arXiv:1712.03033

  3. with Michel Bonnefont, Sylvain Golénia, Matthias Keller and Florentin Münch
    Magnetic sparseness and Schrödinger operators on graphs
    arXiv:1711.10418

  4. with Florentin Münch and Norbert Peyerimhoff
    Rigidity properties of the hypercube via Bakry-Émery curvature
    arXiv:1705.06789

  5. with Fatihcan M. Atay
    Cheeger constants, structural balance, and spectral clustering analysis for signed graphs
    arXiv:1411.3530, MPI MiS Preprint 111/2014

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

  7. 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 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£Ĵaccepted.
    arXiv

  2. 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£Ĵaccepted.
    arXiv

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

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

  5. 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

  6. with Michela Egidi, Florentin Münch and Norbert Peyerimhoff
    Ricci curvature and eigenvalue estimates for the magnetic Laplacian on manifolds
    Communications in Analysis and Geometry£Ĵaccepted.
    arXiv

  7. 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

  8. 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

  9. with David Cushing and Norbert Peyerimhoff
    Bakry-Émery curvature functions of graphs
    Canadian Journal of Mathematics , accepted
    link, arXiv

  10. 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

  11. 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

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

  13. 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

  14. 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

  15. 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

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

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

  18. 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

  19. 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

  20. 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

  21. 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