Real Algebraic and Analytic Geometry |

On the the total curvatures of a tame function.

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Submission: 2007, September 12.

*Abstract:
Given a definable function f, enough differentiable, we study the
continuity of the total curvature function t --> K(t), total curvature of the level {f=t}, and the total
absolute curvature function t-->|K| (t), total absolute curvature of the level {f=t}. We show they admits at
most finitely many discontinuities.*

Mathematics Subject Classification (2000): 03C64, 53B20.

Keywords and Phrases: Gauss curvature, Hausdorff Limits, o-minimal.

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