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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 f…
math.CV2024
Asympotitcs for Some Singular Monge-Ampère Equations
Nicholas McCleerey
Given a psh function and a smooth, bounded , it is known that one can solve the Monge-Ampère equation , wi…
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…