Riemannian空间和热带几何的m-多势理论
m-Pluripotential Theory on Riemannian Spaces and Tropical Geometry
摘要：
在这项研究中，我们将$m$ -多能理论的概念推广到黎曼超空间形式主义。由于在这种情况下，正的超流和热带品种是密切相关的，我们试图了解相对容量的概念与热带超曲面的交叉。将Cartan的经典拟连续性结果推广到黎曼空间的$m$ -次调和函数，最后引入了$m$ -下调和函数的指标，并给出了它们的Newton数的几何刻画.
英文摘要：
In this study we extend the concepts of $m$-pluripotential theory to the Riemannian superspace formalism. Since in this setting positive supercurrents and tropical varieties are closely related, we try to understand the relative capacity notion with respect to the intersection of tropical hypersurfaces. Moreover, we generalize the classical quasicontinuity result of Cartan to $m$-subharmonic functions of Riemannian spaces and lastly we introduce the indicators of $m$-subharmonic functions and give a geometric characterization of their Newton numbers.
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