English

Copolar convexity

Complex Variables 2018-02-16 v2

Abstract

We introduce a new operation, copolar addition, on unbounded convex subsets of the positive orthant of real euclidean space 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 non-constant geodesic curve between two toric relative extremal functions.

Keywords

Cite

@article{arxiv.1701.01002,
  title  = {Copolar convexity},
  author = {Alexander Rashkovskii},
  journal= {arXiv preprint arXiv:1701.01002},
  year   = {2018}
}

Comments

Bugs fixed. Relations to complex interpolated spaces added

R2 v1 2026-06-22T17:40:54.223Z