m-Pluripotential Theory on Riemannian Spaces and Tropical Geometry

2018/08/23 by Sibel Sahin, Sahin, Sibel
Mathematics · #14T05 #31C12 #31C15 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:14T05 #msc:31C12 #msc:31C15

paper · pdf · doi:10.48550/arxiv.1808.07709

11 pages

arxiv created 2019/09/17 · arxiv updated 2019/09/18

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.

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• Superforms, supercurrents, minimal manifolds and Riemannian geometry
• The Tropical Superpotential For ℙ²
• Super currents and tropical geometry
• Pluripotential theory for tropical toric varieties and non-archimedean Monge-Ampére equations
• On quaternionic pluripotential theory associated to quaternionic m-subharmonic functions