2023/06/25 by Tomoya Akamatsu, Akamatsu, Tomoya · 1 citation
Mathematics · Medicine · Physics and Astronomy · #05C12 #47H04 #Advanced Differential Geometry Research #Advanced Neuroimaging Techniques and Applications #Combinatorics (math.CO) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Primary 51F30 #Secondary 05C65
paper · doi:10.48550/arxiv.2306.14084
openalex publication_date 2023/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Ollivier and Lin--Lu--Yau established the theory of graph Ricci curvature (LLY curvature) via optimal transport on graphs. Ikeda--Kitabeppu--Takai--Uehara introduced a new distance called the Kantorovich difference on hypergraphs and generalized the LLY curvature to hypergraphs (IKTU curvature). As the LLY curvature can be represented by the graph Laplacian by Münch--Wojciechowski, Ikeda--Kitabeppu--Takai--Uehara conjectured that the IKTU curvature has a similar expression in terms of the hypergraph Laplacian. In this paper, we introduce a variant of the Kantorovich difference inspired by the above conjecture and study the Ricci curvature associated with this distance (wIKTU curvature). Moreover, for hypergraphs with a specific structure, we analyze a quantity C(x,y) at two distinct vertices x,y defined by using the hypergraph Laplacian. If the resolvent operator converges uniformly to the identity, then C(x,y) coincides with the wIKTU curvature along x,y.