collaborators

10 papers

math.CV2026

Entire solutions of higher order Briot-Bouquet equations

Alexandre Eremenko, Tuen Wai Ng, Teng Zhang

For a meromorphic function in the complex plane, we determine when and are algebraically dependent. This happens precisely when belongs to the class of el…

math.DG2026

Umbilic slopes and cubic Weingarten surfaces

Haoxuan Cheng

We study umbilic slopes and the global classification of cubic Weingarten surfaces. For a smooth surface in Euclidean three-space, a nonconstant principal curvature germ with a uni…

math.DG2026

Bounded curvature manifolds without Euclidean isometric immersions of bounded mean curvature

Haoxuan Cheng

For every integer , we construct a smooth complete Riemannian metric on with full curvature norm at most one and injectivity radius at least one for whi…

math.DG2026

A counterexample to Yau's bounded-mean-curvature embedding question

Haoxuan Cheng

Yau asked whether every complete Riemannian manifold with bounded Ricci curvature and positive injectivity radius admits an isometric embedding into some Euclidean space with bound…

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…