We give a state-of-the-art survey of investigations concerning multivariate polynomial inequalities. A satisfactory theory of such inequalities has been developed due to applications of both the Gabrielov-Hironaka-Łojasiewicz subanalytic geometry and pluripotential methods based on the complex Monge-Ampère operator. Such an approach permits one to study various inequalities for polynomials restricted not only to nice (nonpluripolar) compact subsets of ℝⁿ or ℂⁿ but also their versions for pieces of semialgebraic sets or other "small" subsets of ℝⁿ (ℂⁿ).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc72-0-16,
author = {W. Ple\'sniak},
title = {Multivariate polynomial inequalities viapluripotential theory and subanalytic geometry methods},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {251-261},
zbl = {1109.32007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc72-0-16}
}
W. Pleśniak. Multivariate polynomial inequalities viapluripotential theory and subanalytic geometry methods. Banach Center Publications, Tome 72 (2006) pp. 251-261. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc72-0-16/