11 papers
Signed dual graphs and face spectral gaps of Cayley 2-complexes
Bobo Hua, Yong Lin, Tao Wang +1
We construct a weighted signed dual multigraph for the Cayley -complex of a finite presentation and represent its face Laplacian as a signed graph Laplacian with a diag…
Solvability of Semilinear Elliptic Equations on Infinite Graphs
Bobo Hua, Yong Lin, Haohang Zhang
We develop a constructive method for solving semilinear elliptic equations on locally finite, connected infinite graphs with layered structure. Using Eidelheit's…
The Ollivier Ricci flow with prescribed curvature on infinite graphs
Bobo Hua, Yong Lin, Shuang Liu
In this paper, we consider the Ricci flow with prescribed curvature on infinite graphs, which reads as \begin{equation*}\label{flow-equation3} \frac{d}{dt}ω(t)=-(κ(t)-κ^*)ω(t),~~ t…
A generalized Cheeger inequality and the Steklov Problem on finite graphs
Bobo Hua, Supanat Kamtue, Shiping Liu +2
We prove generalized Cheeger inequalities for eigenvalues of Laplacians for reversible Markov chains. Then we apply Hassannezhad and Miclo's convergence result to obtain Jammes Che…
On the Ricci flow on Trees
Shuliang Bai, Bobo Hua, Yong Lin +1
In this paper, we study the evolution of metrics on finite trees under continuous-time Ricci flows based on the Lin-Lu-Yau version of Ollivier Ricci curvature. We analyze long-time…
On a magneto-spectral invariant on finite graphs
Chunyang Hu, Bobo Hua, Supanat Kamtue +3
In this paper, we introduce a magneto-spectral invariant for finite graphs. This invariant vanishes on trees and is maximized by complete graphs. We compute this invariant for cycl…
Inequalities between Dirichlet and Neumann Eigenvalues on Surfaces
Bobo Hua, Florentin Münch, Haohang Zhang
For a bounded Lipschitz domain in a Riemannian surface satisfying certain curvature condition, we prove that where ( resp.) is the -…
Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs
Bobo Hua, Ruowei Li
We introduce the discrete poly-Laplace operator on a subgraph with Dirichlet boundary condition. We obtain upper and lower bounds for the sum of the first Dirichlet eigenvalues…
Cheeger type inequalities associated with isocapacitary constants on graphs
Bobo Hua, Florentin Münch, Tao Wang
In this paper, we introduce Cheeger type constants via isocapacitary constants introduced by Maz'ya to estimate first Dirichlet, Neumann and Steklov eigenvalues on a finite subgrap…
A version of Bakry-Émery Ricci flow on a finite graph
Bobo Hua, Yong Lin, Tao Wang
In this paper, we study the Bakry-Émery Ricci flow on finite graphs. Our main result is the local existence and uniqueness of solutions to the Ricci flow. We prove the long-time co…
Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature II
Bobo Hua, Juergen Jost
In a previous paper Hua-Jost-Liu, we have applied Alexandrov geometry methods to study infinite semiplanar graphs with nonnegative combinatorial curvature. We proved the weak relat…