Real Algebraic and Analytic Geometry

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233. V. Grandjean:
On the the total curvatures of a tame function.


Submission: 2007, September 12.

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.

Full text, 17p.: dvi 78k, ps.gz 203k, pdf 256k.

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