A remark on the Alexandrov-Fenchel inequality
Complex Variables
2018-02-13 v2 Algebraic Geometry
Functional Analysis
Metric Geometry
Abstract
In this article, we give a complex-geometric proof of the Alexandrov-Fenchel inequality without using toric compactifications. The idea is to use the Legendre transform and develop the Brascamp-Lieb proof of the Pr\'ekopa theorem. New ingredients in our proof include an integration of Timorin's mixed Hodge-Riemann bilinear relation and a mixed norm version of H\"ormander's -estimate, which also implies a non-compact version of the Khovanski\u{i}-Teissier inequality.
Keywords
Cite
@article{arxiv.1705.09933,
title = {A remark on the Alexandrov-Fenchel inequality},
author = {Xu Wang},
journal= {arXiv preprint arXiv:1705.09933},
year = {2018}
}
Comments
New version, "on line first" in Journal of Functional Analysis: https://doi.org/10.1016/j.jfa.2018.01.016