Mixed Hessian inequalities and uniqueness in the class $\mathcal{E}(X,\omega,m)$
Complex Variables
2014-04-25 v1 Analysis of PDEs
Differential Geometry
Abstract
We prove a general inequality for mixed Hessian measures by global arguments. Our method also yields a simplification for the case of complex Monge-Amp\`ere equation. Exploiting this and using Ko{\l}odziej's mass concentration technique we also prove the uniqueness of the solutions to the complex Hessian equation on compact K\"ahler manifolds in the case of probability measures vanishing on -polar sets.
Keywords
Cite
@article{arxiv.1404.6202,
title = {Mixed Hessian inequalities and uniqueness in the class $\mathcal{E}(X,\omega,m)$},
author = {Sławomir Dinew and Chinh H. Lu},
journal= {arXiv preprint arXiv:1404.6202},
year = {2014}
}