A form of Alexandrov-Fenchel inequality
type: Item
instance of: scholarly article
title: A form of Alexandrov-Fenchel inequality
zbMATH Open document ID: 1230.52020
author: Pengfei Guan
author: Xinan Ma
author: Xiaohua Zhu
author: Neil S. Trudinger
published in: Pure and Applied Mathematics Quarterly
publication date: 2011-06-07T00:00:00Z
review text: Based on polarity for convex bodies, the authors introduce a class of domains called \(k^*\)-convex, as natural generalization of the usual notion of convex body and related to the Hessian equation on the unit sphere by the distance function. The authors derive a form of the Aleksandrov-Fenchel inequality for such domains, and they even prove a uniqueness theorem for the Hessian equation (yielding also a generalization of the classical Aleksandrov-Fenchel-Jessen theorem). They use an interesting mixture of methods (using, e.g., hyperbolic polynomial theory).
reviewed by: Horst Martini
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 26B25
zbMATH DE Number: 5904811
zbMATH Keywords: Aleksandrov-Fenchel inequality
zbMATH Keywords: Aleksandrov-Fenchel-Jessen theorem
zbMATH Keywords: generalized convexity notions
zbMATH Keywords: hyperbolic polynomial theory
zbMATH Keywords: polarization
MaRDI profile type: Publication
full work available at URL: pamq.2010.v6.n4.a2
OpenAlex ID: W2055820640
DOI: 10.4310/PAMQ.2010.V6.N4.A2
description: scientific article; zbMATH DE number 5904811