collaborators

5 papers

math.DG2026

A numerical criterion for complex Hessian type equations on projective manifolds

Gao Chen, Sijie Nie, Yulun Xu

We prove a Nakai-Moishezon-type criterion for complex Hessian-type equations on projective manifolds whose associated degree- polynomials are strongly strictly right-Noetherian.…

math.DG2025

The uniqueness of Poincaré type constant scalar curvature Kähler metric

Yulun Xu, Kai Zheng

Let be a smooth divisor on a closed Kähler manifold . First, we prove that Poincaré type constant scalar curvature Kähler (cscK) metric with a singularity at is uniqu…

math.DG2025

The uniqueness of Poincaré type extremal Kähler metric

Yulun Xu

Let be a smooth divisor on a closed Kähler manifold . Suppose that . We prove that the Poincaré type extremal Kähler metric with a cusp singularity at $D…

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.AP2025

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…