m-Pluripotential theory on Riemannian spaces and tropical geometry

Abstract

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.

Analysis of the Influence of Grating Plate on the Internal Illumination Uniformity of Zigzag Photovoltaic Greenhouse

“…In fact, the light intensity of the outdoors changes at any time [21], the cloud layer is always moving, and the measurement process takes time, which makes the measurement results not exactly the same as the conjecture. Meanwhile, considering the evaporation of water vapor is the highest when the solar altitude angle at noon, the blocking of water vapor will also affect the measurement results [22,[26][27][28]. shows the light uniformity and variation coefficient in the model greenhouse at different time periods [23] when the grating plate and glass are used as light-transmitting components.…”

$m$-potential theory and $m$-generalized Lelong numbers associated with $m$-positive supercurrents

“…Denote by C m the set of m-convex functions. Next, let us recall some basic facts about m-convex functions due to S ¸ahin [15]:…”

“…Thanks to S ¸ahin [15], the function u s is also m-convex. Now, it is clear that u s = Aψ on L ∩ (Ω Ω µ A ), hence Stokes formula implies…”

“…). It follows by S ¸ahin [15] that each v j i is m-convex. Denote by (u j,ε i ) 0<ε ε 0 an increasing family of regularization functions converging to…”

“…In the borders cases m = 1 and m = n, we recover the subharmonic and convex functions respectively. In this paper, we consider the notion of m-positivity of superforms and supercurrents introduced firstly by S ¸ahin [15] and next by Elkhadhra and Zahmoul [8]. Besides the introduction, this paper has four sections.…”