We introduce a fully nonlinear PDE with a differential form, which unifies several important
equations in Kähler geometry including Monge-Ampère equations, J-equations, inverse σ k …

We prove that if a level set of a degree n general inverse σ k equation f (λ 1,⋯, λ n):= λ 1⋯ λ
n−∑ k= 0 n− 1 ck σ k (λ)= 0 is contained in q+ Γ n for some q∈ R n, where ck are real …

Abstract The Special Lagrangian Potential Equation for a function u on a domain Ω ⊂ R^ n
Ω⊂ R n is given by tr {\arctan (D^ 2\, u)\}= θ tr arctan (D 2 u)= θ for a contant θ ∈ (-n π\over …

In this paper, we show that the deformed Hermitian Yang-Mills (dHYM) equation on a
rational homogeneous variety, equipped with any invariant K\"{a} hler metric, always admits …

Let (M, ω) be a compact connected Kähler manifold of complex dimension four and let [χ]∈
H 1, 1 (M; R). We confirm the conjecture by Collins–Jacob–Yau [8] of the solvability of the …

In this thesis we study the principle that extremal objects in differential geometry correspond
to stable objects in algebraic geometry. In our introduction we survey the most famous …

In this paper, we study the hypercritical deformed Hermitian-Yang–Mills equation on
compact Kähler manifolds and resolve two conjectures of Collins–Yau [Moment maps …

We show that on any compact Kähler surface existence of solutions to the Z-critical equation
can be characterized using a finite number of effective conditions, where the number of …

The main theme of this paper is the Thomas-Yau conjecture, primarily in the setting of
exact,(quantitatively) almost calibrated, unobstructed Lagrangian branes inside Calabi-Yau …

We prove that if there exists a $ C $-subsolution to a constant coefficients strictly $\Upsilon $-
stable general inverse $\sigma_k $ equation, then there exists a unique solution. As a …