An Effective Łojasiewicz Inequality for Real Polynomials

1999/04/28 by János Kollár, Kollár, János
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/9904161

LATEX2e, 9 pages

arxiv created 1999/04/28 · arxiv updated 2009/11/30

Abstract

Let H be the supremum of finitely many real polynomials of degree d and assume that H has a strict local minimum at 0. We prove a Łojasiewicz-type inequality H(x₁,...,x_n) > ||(x₁,...,x_n)||^s where s depends only on d and n. This implies a similar inequality where (x₁,...,x_n) runs through the points of a semi-algebraic set.

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