Real Algebraic and Analytic Geometry |

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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