English

On the total curvatures of a tame function

Differential Geometry 2011-03-04 v2 Logic

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.

Keywords

Cite

@article{arxiv.0708.0465,
  title  = {On the total curvatures of a tame function},
  author = {V. Grandjean},
  journal= {arXiv preprint arXiv:0708.0465},
  year   = {2011}
}
R2 v1 2026-06-21T09:04:32.806Z