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20192026
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math.AP2026

Regularization and Hölder continuity for complex Hessian equations on Hermitian manifolds

Yulun Xu

Let be a compact Hermitian manifold, and let be a symmetric convex cone. We develop a quantitative regularization method for -admissible functions. As an application…

math.AP2025

Viscosity solution to complex Hessian quotient equations

Jingrui Cheng, Yulun Xu

In this paper, we prove the existence of viscosity solutions to complex Hessian equations on compact Hermitian manifolds, assuming the existence of a strict subsolution in the visc…

math.AP2024

Viscosity solution to complex Hessian equations on compact Hermitian manifolds

Jingrui Cheng, Yulun Xu

We prove the existence of viscosity solutions to complex Hessian equations on a compact Hermitian manifold that satisfy a determinant domination condition. This viscosity solution…

math.AP2023

Interior estimate for small perturbations to the complex Monge-Ampere equation

Jingrui Cheng, Yulun Xu

Let be a bounded, , strictly plurisubharmonic function defined on . Then has a neighborhood in with the following proper…

math.AP2022

Regularization Of -subharmonic Functions And HÖlder Continuity

Jingrui Cheng, Yulun Xu

We use sup-convolution to find upper approximations of a bounded -subharmonic function on a compact Kähler manifold with nonnegative holomorphic bisectional curvature. As an app…