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Copolar convexity

Volume 120 / 2017

Alexander Rashkovskii Annales Polonici Mathematici 120 (2017), 83-95 MSC: Primary 32U15; Secondary 32U20, 52A20, 52A39. DOI: 10.4064/ap170217-4-9 Published online: 13 October 2017


We introduce a new operation, copolar addition, on unbounded convex subsets of the positive orthant of ${\mathbb R}^n$ and establish convexity of the covolumes of the corresponding convex combinations. The proof is based on a technique of geodesics of plurisubharmonic functions. As an application, we show that there are no relative extremal functions inside a nonconstant geodesic curve between two toric relative extremal functions.


  • Alexander RashkovskiiTek/Nat
    University of Stavanger
    4036 Stavanger, Norway

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