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From the discrete to the continuous, from simplicial complexes to Riemannian manifolds. Approximating flows and cuts on manifolds by discrete versions
Marzieh Eidi, Juergen Jost, Dong Zhang
Many fundamental structures of Riemannian geometry have found discrete counterparts for graphs or combinatorial ones for simplicial complexes. These include those discussed in this…
Combinatorial Courant-Fischer-Weyl Minimax Principle on Cheeger -constants of Weighted Forests
Zijun Meng, Dong Zhang
We present several max-min and minimax characterizations of Cheeger -constants in weighted forests, thereby providing the first combinatorial analogue of the Courant-\\Fischer-W…
Finite projective planes meet spectral gaps
Yuhan Guo, Dong Zhang
We show that for any connected graph with maximum degree , the spectral gap from with respect to the adjacency matrix is at most , with equality if and o…
Notes on suu Chern-Simons theory and Torsional Newton-Cartan gravity
Yang Lei, Dong Zhang
In this study, we investigate three-dimensional torsional Newton-Cartan (TNC) gravity by gauging the suu algebra and construct its action using the Chern-Simons t…
Nonlinear spectral graph theory
Piero Deidda, Francesco Tudisco, Dong Zhang
Nonlinear spectral graph theory is an extension of the traditional (linear) spectral graph theory and studies relationships between spectral properties of nonlinear operators defin…