5 papers
Lin-Lu-Yau Ricci curvature on hypergraphs
Yulu Tian, Liang Zhao
In this paper, we introduce a unified framework for defining Lin-Lu-Yau (LLY) Ricci curvature on both undirected and directed hypergraphs. By establishing upper bounds and monotoni…
Community detection of hypergraphs by Ricci flow
Yulu Tian, Jicheng Ma, Yunyan Yang +1
Community detection in hypergraphs is both instrumental for functional module identification and intricate due to higher-order interactions among nodes. We define a hypergraph Ricc…
A note for W^{1,p}(V) and W_0^{1,p}(V) on a locally finite graph
Yulu Tian, Liang Zhao
In this paper, we investigate the Sobolev spaces W^{1,p}(V) and W_0^{1,p}(V) on a locally finite graph G=(V,E), which are fundamental tools when we apply the variational methods to…
Calculus of variations on hypergraphs
Mengqiu Shao, Yulu Tian, Liang Zhao
We have established a coherent framework for applying variational methods to partial differential equations on hypergraphs, which includes the propositions of calculus and function…
Normalized solution to the nonlinear p-Laplacian equation with an L^2 constrain: mass supercritical case
Yulu Tian, Deng-Shan Wang, Liang Zhao
In this paper, we study the existence of ground state solutions to the following p-Laplacian equation in some dimension with an constraint: \begin{equation*} \begin{…