On the total curvatures of a tame function

Author： Grandjean Vincent  

Publisher： Springer Publishing Company

ISSN： 1678-7544

Source： Bulletin of the Brazilian Mathematical Society, Vol.39, Iss.4, 2008-12, pp. : 515-535

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Abstract

Given a definable function f: ℜ n ↦ ℜ, enough differentiable, we study the continuity of the total curvature function t → K(t), total curvature of the level f −1(t), and the total absolute curvature function t → |K|(t), total absolute curvature of the level f −1(t). We show they admits at most finitely many discontinuities.

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