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Gauss-Kronecker Curvature and equisingularity at infinity of definable families | | Nicolas Dutertre
; Vincent Grandjean
; | | Date: |
19 Mar 2019 | | Abstract: | Assume given a polynomially bounded o-minimal structure expanding the real
numbers. Let $(T_s)_{sin mathbb{R}}$ be a globally definable one parameter
family of $C^2$-hypersurfaces of $mathbb{R}^n$. Upon defining the notion of
generalized critical value for such a family we show that the functions $s o
|K(s)|$ and $s o K(s)$, respectively the total absolute Gauss-Kronecker and
total Gauss-Kronecker curvature of $T_s$, are continuous in any neighbourhood
of any value which is not generalized critical. In particular this provides a
necessary criterion of equisingularity for the family of the levels of a real
polynomial. | | Source: | arXiv, 1903.8001 | | Services: | Forum | Review | PDF | Favorites | |
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