Complex Hessian equations with prescribed singularity on compact K\"ahler manifolds

Chinh H. Lu; Van-Dong Nguyen

Complex Hessian equations with prescribed singularity on compact K\"ahler manifolds

Complex Variables 2019-09-06 v1 Differential Geometry

Authors: Chinh H. Lu , Van-Dong Nguyen

Abstract

Let $(X,\omega)$ be a compact K\"ahler manifold of dimension $n$ and fix $1\leq m\leq n$ . We prove that the total mass of the complex Hessian measure of $\omega$ - $m$ -subharmonic functions is non-decreasing with respect to the singularity type. We then solve complex Hessian equations with prescribed singularity, and prove a Hodge index type inequality for positive currents.

Keywords

kähler manifolds kähler metrics

Cite

@article{arxiv.1909.02469,
  title  = {Complex Hessian equations with prescribed singularity on compact K\"ahler manifolds},
  author = {Chinh H. Lu and Van-Dong Nguyen},
  journal= {arXiv preprint arXiv:1909.02469},
  year   = {2019}
}

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