Currently displaying 1 – 2 of 2

Showing per page

Order by Relevance | Title | Year of publication

A gradient inequality at infinity for tame functions.

Didier D'Acunto;  Vincent Grandjean — 2005

Revista Matemática Complutense

Let f be a C function defined over R 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 C we use this inequality to discuss the trivialization by the gradient flow of f in a neighborhood of a regular asymptotic critical level.

On gradient at infinity of semialgebraic functions

Didier D'Acunto;  Vincent Grandjean — 2005

Annales Polonici Mathematici

Let f: ℝⁿ → ℝ be a C² semialgebraic function and let c be an asymptotic critical value of f. We prove that there exists a smallest rational number ϱ c ≤ 1 such that |x|·|∇f| and | f ( x ) - c | ϱ c are separated at infinity. If c is a regular value and ϱ c < 1 , then f is a locally trivial fibration over c, and the trivialisation is realised by the flow of the gradient field of f.

Page 1

Download Results (CSV)