q-Plurisubharmonicity and q-pseudoconvexity in cn

We generalize classical results for plurisubharmonic functions and hyperconvex domain to $q$-plurisubharmonic functions and $q$-hyperconvex domains. We show, among other things, that $B_q$-regular domains are $q$-hyperconvex. Moreover, some smoothing results for $q$-plurisubharmonic functions are also given

L'Enveloppe locale des perturbations d'une union de plans totalement réels qui se coupent en une droite réele

In this note by using techniques similar to that of [2] and [3], we study the local polynomial convexity of perturbation of union of two totally real planes meeting along a real line

Solutions to weighted complex m-Hessian Equations on domains in Cn

In this paper, we first study the comparison principle for the operator $H_{\chi,m}$. This result is used to solve certain weighted complex $m-$ Hessian equations.Comment: 25 page

Maximal subextension and approximation of m−m- subharmonic function

In this paper, we first study subextensions in the classes $\mathcal{F}_{m}(\Omega)$ and $\mathcal{E}_{m,\chi}(\Omega)$. These results are then used to study approximation in the classes $\mathcal{F}_{m}(\Omega)$ and $\mathcal{E}_{m,\chi}(\Omega)$.Comment: 24 page