论文标题
复杂的Hessian操作员加权绿色功能
Weighted Green functions for complex Hessian operators
论文作者
论文摘要
令$ 1 \ leq m \ leq n $为两个固定整数。令$ω\ subset \ mathbb c^n $为有限的$ M $ -HYPERCONVEX域和$ \ Mathcal A \ subsetω\ times] 0，+ \ infty [$一组有限的加权电线杆。我们定义和研究$ m $ -subharmonic绿色功能的$ω$的属性，并在加权集$ a $附近的规定行为。特别是，我们证明了两个变量$（z，\ mathcal a）$在公制空间$ \ barω\ times \ times \ Mathcal f $中的指数绿色功能的连续性均匀，其中$ \ Mathcal f $是合适的一组套装，包括$ω\ fimes的加权电池，+ \ fly [+ \ iffty] 0，与infty [$ fectept [$ fectept [$ fecte drocked datcort]此外，我们对其连续性模量进行了准确的估计。我们的结果概括并改善了有关P. Lelong的Pluricomplex绿色功能DU的先前结果。
Let $1\leq m\leq n$ be two fixed integers. Let $Ω\Subset \mathbb C^n$ be a bounded $m$-hyperconvex domain and $\mathcal A \subset Ω\times ]0,+ \infty[$ a finite set of weighted poles. We define and study properties of the $m$-subharmonic Green function of $Ω$ with prescribed behaviour near the weighted set $A$. In particular we prove uniform continuity of the exponential Green function in both variables $(z,\mathcal A)$ in the metric space $\bar Ω\times \mathcal F$, where $\mathcal F$ is a suitable family of sets of weighted poles in $Ω\times ]0,+ \infty[$ endowed with the Hausdorff distance. Moreover we give a precise estimates on its modulus of continuity. Our results generalize and improve previous results concerning the pluricomplex Green function du to P. Lelong.
