We prove that generalised Monge-Ampère equations (a family of equations which includes
the inverse Hessian equations like the J-equation, as well as the Monge-Ampère equation) …

We derive a priori 2nd-order estimates for fully nonlinear elliptic equations that depend on
the gradients of solutions on compact Hermitian manifolds, which is a crucial step in solving …

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 an existence result for the deformed Hermitian Yang–Mills equation for the full
admissible range of the phase parameter, ie, 𝜃^∈(π 2, 3 π 2), on compact complex three …

We study the deformed Hermitian-Yang-Mills equation on the blowup of complex projective
space. Using symmetry, we express the equation as an ODE which can be solved using …

We solve the Dirichlet problem for $ k $-Hessian equations on compact complex manifolds
with boundary, given the existence of a subsolution. Our method is based on a second order …

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 …

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 …

We introduce a geometric approach to the construction of moment maps in finite and infinite-
dimensional complex geometry. We apply this to two settings: K\" ahler manifolds and …

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 …