Bobo Hua

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20242026

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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: $κ = - λ_{m a x} (R_{T})$ . We show t…

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 $λ_{m a x} (R_{T})$ determines the sign of a discrete Einstein metric cu…

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…