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math.DG2024
On the uniqueness of Poincaré type cscK metrics
Yulun Xu, Kai Zheng
Let be a compact Kähler manifold with a divisor which may have simple normal crossings. We prove that the -energy is convex on the space of Poincaré type Kähler metrics.…
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…