An Effective ojasiewicz Inequality for Real Polynomials
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 ojasiewicz-type inequality H(x1,...,xn) > ||(x1,...,xn)||s where s depends only on d and n. This implies a similar inequality where (x1,...,xn) runs through the points of a semi-algebraic set.
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