3 papers
math.DG2026
Alternative proof of the gradient estimate for complex Hessian equations
Jianchun Chu, Yaxiong Liu
For complex Hessian equations on compact Kähler manifolds, we give an alternative proof of the gradient estimate without using blow-up argument, and clarify its dependence on the r…
math.CV2026
Some variational problems for the complex Monge--Amp{è}re operator
Jianchun Chu, Yaxiong Liu, Nicholas McCleerey +1
We consider the Dirichlet problem for the complex Monge--Ampère equation on strongly pseudoconvex Kähler manifolds when the right-hand side is decreasing in the solution. Using flo…
math.CV2024
The Eigenvalue Problem for the Complex Hessian Operator on -Pseudoconvex Manifolds
Jianchun Chu, Yaxiong Liu, Nicholas McCleerey
We establish -regularity and uniqueness of the first eigenfunction of the complex Hessian operator on strongly -pseudoconvex manifolds, along with a variational formula…