A Gradient Inequality at Infinity for Tame Functions - D’acunto, Didier; Grandjean, Vincent (Revista Matemática Complutense, 2005)
Let f be a C1 function defined over Rn and definable in a given o-minimal structure M expanding the real field. We prove here a gradient-like inequality at infinity in a neighborhood of an asymptotic critical value c. When f is C2 we use this inequality to discuss the trivialization by the gradient flow of f in a neighborhood of a regular asymptotic critical level.