On the total curvatures of a tame function
arXiv:0708.0465 · doi:10.1007/s00574-008-0002-8
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.