Real Algebraic and Analytic Geometry

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151. Didier D'Acunto, Vincent Grandjean:
A Gradient Inequality at infinity for tame functions.

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Submission: 2004, December 17.

Given a definable function F enough differentiable defined over R^n, we find a Lojasiewicz type inequality at infinity satisfied by the gradient of the function F in a neighbourhood of an asymptotic critical value c. We use this result to discuss sufficient conditions to trivialise by the gradient flow of F over a neighbourhood of c.

Mathematics Subject Classification (2000): 03C64 34A26 34C08.

Keywords and Phrases: Lojasiewicz, o-minimality, gradient, asymptotic critical values.

Full text, 8p.: dvi 37k, ps.gz 148k, pdf 209k.

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