On the total curvatures of a tame function

Details On the total curvatures of a tame function On the total curvatures of a tame function

2007-08-03

arxiv.org/abs/0708.0465v2

Bull. Braz. Math. Soc. (N.S.) 39 (2008), no. 4, 515-535

Mathematics

Differential Geometry

Scientific paper

10.1007/s00574-008-0002-8

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.

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