no. 5
Whitney stratifications and the continuity of local Lipschitz–Killing curvatures
[Stratifications de Whitney et la continuité des courbures Lipschitz–Killing locales]
Nguyen, Nhan1 ; Valette, Guillaume2
1 ICMC, Universidade de São Paulo Avenida trabalhador São-Carlense, 400-Centro, 13566-590 – São Carlos, São Paulo (Brazil)
2 Instytut Matematyki, Uniwersytetu Jagiellońskiego, ul. S. Łojasiewicza 6, 30-348 Kraków (Poland)
Annales de l'Institut Fourier, Tome 68 (2018) no. 5, pp. 2253-2276.

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 :
Révisé le :
Accepté le :
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DOI : 10.5802/aif.3208
Classification : 14B15, 14B10, 32B20, 57R45
Keywords: o-minimal structures, definable sets, stratifications, local Lipschitz–Killing curvatures
Mot clés : semblable banalité, autosimilarité logarithmique, loi de Gauß

Nguyen, Nhan 1 ; Valette, Guillaume 2

1 ICMC, Universidade de São Paulo Avenida trabalhador São-Carlense, 400-Centro, 13566-590 – São Carlos, São Paulo (Brazil)
2 Instytut Matematyki, Uniwersytetu Jagiellońskiego, ul. S. Łojasiewicza 6, 30-348 Kraków (Poland)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.3208/

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