Whitney stratifications and the continuity of local Lipschitz–Killing curvatures

Nguyen, Nhan; Valette, Guillaume

doi:10.5802/aif.3208

Whitney stratifications and the continuity of local Lipschitz–Killing curvatures [ Stratifications de Whitney et la continuité des courbures Lipschitz–Killing locales ]

Nguyen, Nhan ; Valette, Guillaume

Annales de l'Institut Fourier, Tome 68 (2018) no. 5, pp. 2253-2276.

Résumé
Abstract

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.

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.

Reçu le : 2017-01-16
Révisé le : 2017-07-10
Accepté le : 2017-11-06
Publié le : 2018-11-22

DOI : https://doi.org/10.5802/aif.3208
Classification : 14B15, 14B10, 32B20, 57R45
Mots clés : semblable banalité, autosimilarité logarithmique, loi de Gauß

@article{AIF_2018__68_5_2253_0,
     author = {Nguyen, Nhan and Valette, Guillaume},
     title = {Whitney stratifications and the continuity of local Lipschitz--Killing curvatures},
     journal = {Annales de l'Institut Fourier},
     pages = {2253--2276},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {68},
     number = {5},
     year = {2018},
     doi = {10.5802/aif.3208},
     language = {en},
     url = {archive.numdam.org/item/AIF_2018__68_5_2253_0/}
}

Nguyen, Nhan; Valette, Guillaume. Whitney stratifications and the continuity of local Lipschitz–Killing curvatures. Annales de l'Institut Fourier, Tome 68 (2018) no. 5, pp. 2253-2276. doi : 10.5802/aif.3208. http://archive.numdam.org/item/AIF_2018__68_5_2253_0/

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