On a convex level set of a plurisubharmonic function and the support of\n the Monge-Amp `ere current

2014/10/14 by Yusaku Tiba, Tiba, Yusaku
Mathematics · #32U15 #32U35 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1410.3785

openalex publication_date 2014/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study a geometric property of a continuous plurisubharmonic\nfunction which is a solution of the Monge-Amp `ere equation and has a convex\nlevel set. To prove our main theorem, we show a minimum principle of a maximal\nplurisubharmonic function. By using our results and Lempert's results, we show\na relation between the supports of the Monge-Amp `ere currents and complex\nk-extreme points of closed balls for the Kobayashi distance in a bounded\nconvex domain in \ℂⁿ.\n

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