Real Algebraic and Analytic Geometry
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202. Vincent Grandjean:
Triviality at infinity of real 3-space polynomial functions with cone-like ends.

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Submission: 2006, July 18.

Abstract:
Let $f:\mathbb{R}^3\to\mathbb{R}$ be a polynomial function with cone-like ends. We give a necessary and sufficient condition to trivialise the function over a neighbourhood of a regular value $c$ in terms of the continuity of the total curvature of the levels nearby $c$.

Mathematics Subject Classification (2000): 14P10, 57R70.

Keywords and Phrases: Semialgebraic functions, total curvatures, Morse functions, polar curves, cone-like ends, bifurcation value, asymptotic critical value.

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