Acta Mathematica Vietnamica
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Continuous Solutions for Degenerate Complex Hessian Equation
Hichame Amal
,
Saïd Asserda
,
Manar Bouhssina
Abstract
Let $(X,\omega)$ be an $n$-dimensional compact Kähler manifold and fix an integer $m$ such that $1\leq m\leq n$. Let $\mu$ be a finite Borel measure on $X$ satisfying the conditions $\mathcal{H}_m(\delta, A,\omega)$. We study degenerate complex Hessian equations of the form $(\omega+ dd^{c}\varphi)^{m}\wedge\omega^{n-m}=F(\varphi,.)d\mu$. Under some natural conditions on $F$, we prove that if $0<\delta<\frac{m}{n-m}$, then this equation has a unique continuous solution.