Dekai Zhang

collaborators

3 papers

math.DG2026

Limiting Behavior of a Class of Hermitian Yang--Mills Metrics, II: Exponential Approximation

Jixiang Fu, Dekai Zhang

This paper is a sequel to [9], where the first-named author constructed a family of approximate Hermitian Yang--Mills metrics $H_{0, ε}$ on stable rank-two holomorphic vector bundle…

math.DG2026

A Numerical Criterion for the 2-Hessian Equation on Compact Kähler Manifolds

Jixiang Fu, Dekai Zhang, Ziyi Zhang

We show that a Nakai--Moishezon-type criterion associated with the complex $2$ -Hessian equation produces a Gauduchon class. In complex dimension three, this numerical criterion is…

math.DG2025

The Critical LYZ Equation in Kähler Geometry

Jixiang Fu, Shing-Tung Yau, Dekai Zhang

We establish the existence of smooth solutions for the LYZ equation at the critical phase $θ = (n - 2) \frac{π}{2}$ , thereby solving the critical case of a problem posed by Collins-Jacob-…