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

Chinh H. Lu; Van-Dong Nguyen

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arXiv · 1909.02469

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

Chinh H. Lu·Van-Dong Nguyen

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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.

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Chinh H. Lu, Van-Dong Nguyen. 2019-09-05. Complex Hessian equations with prescribed singularity on compact K\"ahler manifolds. https://arxiv.org/abs/1909.02469

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