Outputs (5)

Bakry-Émery curvature sharpness and curvature flow in finite weighted graphs: theory (2025)
Journal Article
Cushing, D., Kamtue, S., Liu, S., Münch, F., Peyerimhoff, N., & Snodgrass, B. (2025). Bakry-Émery curvature sharpness and curvature flow in finite weighted graphs: theory. manuscripta mathematica, 176(1), Article 11. https://doi.org/10.1007/s00229-024-01606-7

In this sequence of two papers, we introduce a curvature flow on (mixed) weighted graphs which is based on the Bakry-Émery calculus. The flow is described via a time-continuous evolution through the weighting schemes. By adapting this flow to preserv... Read More about Bakry-Émery curvature sharpness and curvature flow in finite weighted graphs: theory.

Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians (2015)
Journal Article
Lange, C., Liu, S., Peyerimhoff, N., & Post, O. (2015). Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians. Calculus of Variations and Partial Differential Equations, 54(4), 4165-4196. https://doi.org/10.1007/s00526-015-0935-x

We discuss a Cheeger constant as a mixture of the frustration index and the expansion rate, and prove the related Cheeger inequalities and higher order Cheeger inequalities for graph Laplacians with cyclic signatures, discrete magnetic Laplacians on... Read More about Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians.

Spectral distances on graphs (2015)
Journal Article
Gu, J., Hua, B., & Liu, S. (2015). Spectral distances on graphs. Discrete Applied Mathematics, 190-191, 56-74. https://doi.org/10.1016/j.dam.2015.04.011

By assigning a probability measure via the spectrum of the normalized Laplacian to each graph and using Lp Wasserstein distances between probability measures, we define the corresponding spectral distances dp on the set of all graphs. This approach c... Read More about Spectral distances on graphs.

Multi-way dual Cheeger constants and spectral bounds of graphs (2014)
Journal Article
Liu, S. (2015). Multi-way dual Cheeger constants and spectral bounds of graphs. Advances in Mathematics, 268, 306-338. https://doi.org/10.1016/j.aim.2014.09.023

We introduce a set of multi-way dual Cheeger constants and prove universal higher-order dual Cheeger inequalities for eigenvalues of normalized Laplace operators on weighted finite graphs. Our proof proposes a new spectral clustering phenomenon deduc... Read More about Multi-way dual Cheeger constants and spectral bounds of graphs.

Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature (2013)
Journal Article
Hua, B., Jost, J., & Liu, S. (2013). Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature. Journal für die reine und angewandte Mathematik, 2015(700), 1-36. https://doi.org/10.1515/crelle-2013-0015

We apply Alexandrov geometry methods to study geometric analysis aspects of infinite semiplanar graphs with nonnegative combinatorial curvature. We obtain the metric classification of these graphs and construct the graphs embedded in the projective p... Read More about Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature.