7 papers
Divisorial Rigidity and Regularity of Boundary Cases for the Supercritical LYZ Equation
Jixiang Fu, Shing-Tung Yau, Dekai Zhang +1
We study the supercritical LYZ equation on compact Kähler manifolds at the boundary of stability. Under numerical semistability, we prove a quantitative positivity estimate on the…
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 on stable rank-two holomorphic vector bundle…
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 -Hessian equation produces a Gauduchon class. In complex dimension three, this numerical criterion is…
Limiting behavior of a class of Hermitian Yang-Mills metrics, II: exponential decay
Jixiang Fu
In this note, the geometric set-up, the rank two bundle, the local HYM ansatz, and the global gluing construction are the same as in the preceding work \cite{Fu}. The new point is…
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 , thereby solving the critical case of a problem posed by Collins-Jacob-…
The parabolic quaternionic Monge-Ampère type equation on hyperKähler manifolds
Jixiang Fu, Xin Xu, Dekai Zhang
We prove the long time existence and uniqueness of solution to a parabolic quaternionic Monge-Ampère type equation on a compact hyperKähler manifold. We also show that after normal…
Limiting Behavior of a Class of Hermitian-Yang-Mills Metrics, I
Jixiang Fu
This paper begins to study the limiting behavior of a family of Hermitian Yang-Mills (HYM for brevity) metrics on a class of rank two slope stable vector bundles over a product of…