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.
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