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On a convex level set of a plurisubharmonic function and the support of the Monge–Ampère current

Volume 121 / 2018

Yusaku Tiba Annales Polonici Mathematici 121 (2018), 251-262 MSC: Primary 32U15; Secondary 32U35. DOI: 10.4064/ap180423-14-8 Published online: 12 October 2018


We study a geometric property of a continuous plurisubharmonic function which is a solution of the Monge–Ampère equation and has a convex level set. To prove our main theorem, we show a minimum principle for a maximal plurisubharmonic function. By using our results and Lempert’s results, we show a relation between the supports of the Monge–Ampère currents and complex $k$-extreme points of closed balls for the Kobayashi distance in a bounded convex domain in $\mathbb {C}^{n}$.


  • Yusaku TibaDepartment of Mathematics
    Ochanomizu University
    2-1-1 Otsuka, Bunkyo-ku, Tokyo, Japan

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