论文标题
$ m $ - 电势理论和$ m $属性的Lelong数字与$ M $阳性超电流
$m$-potential theory and $m$-generalized Lelong numbers associated with $m$-positive supercurrents
论文作者
论文摘要
在这项研究中，我们首先定义了与Ben Messaoud和El Mir在复杂环境中所研究的相比，与弱正闭合超流相关的局部潜力。接下来，我们研究$ M $ -Superhessian操作员的定义和连续性，用于无限制的$ M $ -CONVEX函数。作为一个应用程序，我们将以前的工作概括为Demailly-Lelong-Lelong的数字和超级主义设置中的几个相关结果。此外，受到复杂的Hessian理论的强烈启发，我们介绍了Cegrell型类别，以及在$ M $ -CONVEX函数类中对一些$ M $ - 电位结果的概括。
In this study, we first define the local potential associated to a weakly positive closed supercurrent in analogy to the one investigated by Ben Messaoud and El Mir in the complex setting. Next, we study the definition and the continuity of the $m$-superHessian operator for unbounded $m$-convex functions. As an application, we generalize our previous work on Demailly-Lelong numbers and several related results in the superformalism setting. Furthermore, strongly inspired by the complex Hessian theory, we introduce the Cegrell-type classes as well as a generalization of some $m$-potential results in the class of $m$-convex functions.
