4 papers · 1 filter
Curvature Diffusion of Inverse-weight Lin--Lu--Yau Ricci Flow on Finite Trees
Shuliang Bai, Bobo Hua
We study the inverse-weight Lin--Lu--Yau Ricci flow on finite trees, and prove the convergence of the curvature on every edge via its diffusion equation. Moreover, the limiting cur…
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 t…
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 cu…
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…