Whitney stratifications and the continuity of local Lipschitz–Killing curvatures
Annales de l'Institut Fourier, Volume 68 (2018) no. 5, pp. 2253-2276.

In the paper we prove that the local Lipschitz–Killing curvatures of a definable set in a polynomially bounded o-minimal structure are continuous along the strata of a Whitney stratification. Moreover, if the stratification is (w)-regular the local Lipschitz–Killing curvatures are locally Lipschitz in any o-minimal structure.

On montre que les courbures Lipschitz–Killing locales d’un ensemble définissable dans une structure o-minimale polynomialement bornée sont continues le long des strates d’une stratification de Whitney. De plus, si la stratification est (w)-régulière les courbures Lipschitz–Killing locales sont localement lipschitziennes dans une structure o-minimale arbitraire.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3208
Classification: 14B15,  14B10,  32B20,  57R45
Keywords: o-minimal structures, definable sets, stratifications, local Lipschitz–Killing curvatures
License: CC-BY-ND 4.0
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     title = {Whitney stratifications and the continuity of local {Lipschitz{\textendash}Killing} curvatures},
     journal = {Annales de l'Institut Fourier},
     pages = {2253--2276},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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Nguyen, Nhan; Valette, Guillaume. Whitney stratifications and the continuity of local Lipschitz–Killing curvatures. Annales de l'Institut Fourier, Volume 68 (2018) no. 5, pp. 2253-2276. doi : 10.5802/aif.3208. https://aif.centre-mersenne.org/articles/10.5802/aif.3208/

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