Haoxuan Cheng

collaborators

4 papers

math.DG2026

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…

math.DG2026

Edge Subdivision and the Perron Eigenvalue of Tree Ricci Matrices

Shuliang Bai, Haoxuan Cheng, Bobo Hua

The Ricci matrix $R_{T}$ of a finite tree encodes its discrete Einstein metrics via the Perron eigenvector, with Lin-Lu-Yau's Ollivier Ricci curvature: $I^º = - I^»_{m a x} (R_{T})$ . We show…

math.DG2026

Positive-Curvature Discrete Einstein Metrics on Trees

Haoxuan Cheng

For a weighted tree, the Lin--Lu--Yau Ricci curvature admits an explicit formula in terms of the edge weights. Consequently, the constant-curvature equation is equivalent to an eig…

math.DG2026

Spectral Monotonicity under Leaf Attachment and Limiting Behavior in Discrete Einstein Trees

Shuliang Bai, Haoxuan Cheng, Bobo Hua

Let $R_{T}$ be the Ricci matrix of a finite tree $T$ introduced in \cite{BaiChengHua2026}, the largest eigenvalue $I^»_{m a x} (R_{T})$ determines the sign of a discrete Einstein metric c…