121 citations · 538 across the 72 of their papers we have counts for
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Representation Theory of an Infinite Quiver
Raymundo Bautista, Shiping Liu, Charles Paquette
This paper deals with the representation theory of a locally finite quiver in which the number of paths between any two given vertices is finite. We first study some properties of…
Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature
Bobo Hua, Jürgen Jost, Shiping Liu
In the present paper, we apply Alexandrov geometry methods to study geometric analysis aspects of infinite semiplanar graphs with nonnegative combinatorial curvature in the sense o…
Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator
Frank Bauer, Jürgen Jost, Shiping Liu
We prove the following estimate for the spectrum of the normalized Laplace operator on a finite graph , \begin{equation*}1- (1- k[t])^{\frac{1}{t}}\leq λ_1 \leq \cdots \leq…
A proof of the strong no loop conjecture
Kiyoshi Igusa, Shiping Liu, Charles Paquette
The strong no loop conjecture states that a simple module of finite projective dimension over an artin algebra has no non-zero self-extension. The main result of this paper establi…
Ollivier's Ricci curvature, local clustering and curvature dimension inequalities on graphs
Jürgen Jost, Shiping Liu
In this paper, we explore the relationship between one of the most elementary and important properties of graphs, the presence and relative frequency of triangles, and a combinator…