# Wydawnictwa / Banach Center Publications / Wszystkie tomy

## Multivariate polynomial inequalities viapluripotential theory and subanalytic geometry methods

### Tom 72 / 2006

Banach Center Publications 72 (2006), 251-261 MSC: 32B20, 14P05, 32E30, 32U35, 26E10, 41A17. DOI: 10.4064/bc72-0-16

#### Streszczenie

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 $\Bbb R^n$ or $\Bbb C^n$ but also their versions for pieces of semialgebraic sets or other “small” subsets of $\Bbb R^n$ ($\Bbb C^n$).

#### Autorzy

• W. PleśniakInstytut Matematyki
Uniwersytet Jagielloński
Reymonta 4
30-059 Kraków, Poland
e-mail

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