collaborators

6 papers

math.DG2026

Unbounded normalized scalar curvature integrals in dimension four

Haoxuan Cheng

We give counterexamples to Yau's question on normalized scalar curvature integrals in every dimension . For each such , there exists a smooth complete Riemannian metric…

math.DG2026

Singular Rotational Self-Similar Tori for Odd -Curvature Flows

Haoxuan Cheng, Junqi Lai, Guoxin Wei

For every pair of integers with odd, we construct a compact embedded rotational torus in whose homothetic dilations satisfy the unnormalised $σ_k…

math.DG2026

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…

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 be the Ricci matrix of a finite tree introduced in \cite{BaiChengHua2026}, the largest eigenvalue 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…