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arXiv · 1705.09933

A remark on the Alexandrov-Fenchel inequality

Xu Wang
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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 $L^2$-estimate, which also implies a non-compact version of the Khovanski\u{i}-Teissier inequality.

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Xu Wang. 2017-05-28. A remark on the Alexandrov-Fenchel inequality. https://arxiv.org/abs/1705.09933

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