From the 1 of 7 linked papers with an AI index.
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Discrete Einstein metrics on trees
Shuliang Bai, Haoxuan Cheng, Bobo Hua
We establish the existence and uniqueness of discrete Einstein metrics on trees under Lin-Lu-Yau Ricci curvature using Perron-Frobenius theory. We establish a sharp upper bound for…
Edge Subdivision and the Perron Eigenvalue of Tree Ricci Matrices
Shuliang Bai, Haoxuan Cheng, Bobo Hua
The Ricci matrix of a finite tree encodes its discrete Einstein metrics via the Perron eigenvector, with Lin-Lu-Yau's Ollivier Ricci curvature: . We show…
Spectral Monotonicity under Leaf Attachment and Limiting Behavior in Discrete Einstein Trees
Shuliang Bai, Haoxuan Cheng, Bobo Hua
Let be the Ricci matrix of a finite tree introduced in \cite{BaiChengHua2026}, the largest eigenvalue determines the sign of a discrete Einstein metric c…
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…
The weighted Forman and Lin-Lu-Yau Ricci flow on graphs
Shuliang Bai, Shuang Liu, Xin Lai
In this paper, we propose a type of Ricci flow on graphs where the probability distribution for the Lin-Lu-Yau curvature remains constant over time, and also study the related Form…
Ricci Flow on Weighted Digraphs with Balancing Factor
Shuliang Bai, Rui Li, Shuang Liu +1
Ricci curvature and Ricci flow have proven to be powerful tools for analyzing the geometry of discrete structures, particularly on undirected graphs, where they have been applied t…