Geodesic
Copolar convexity
Alexander Rashkovskii1
1 Tek/Nat University of Stavanger 4036 Stavanger, Norway
Annales Polonici Mathematici, Tome 120 (2017) no. 1, pp. 83-95 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ap170217-4-9
Keywords: introduce operation copolar addition unbounded convex subsets positive orthant mathbb establish convexity covolumes corresponding convex combinations proof based technique geodesics plurisubharmonic functions application there relative extremal functions inside nonconstant geodesic curve between toric relative extremal functions

Alexander Rashkovskii 1

1 Tek/Nat University of Stavanger 4036 Stavanger, Norway 
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Alexander Rashkovskii. Copolar convexity. Annales Polonici Mathematici, Tome 120 (2017) no. 1, pp. 83-95. doi: 10.4064/ap170217-4-9

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