Copolar convexity
Volume 120 / 2017
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
Abstract
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.
