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 -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 -régulière les courbures Lipschitz–Killing locales sont localement lipschitziennes dans une structure o-minimale arbitraire.
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Keywords: o-minimal structures, definable sets, stratifications, local Lipschitz–Killing curvatures
Mot 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{\textendash}Killing} curvatures}, journal = {Annales de l'Institut Fourier}, pages = {2253--2276}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {68}, number = {5}, year = {2018}, doi = {10.5802/aif.3208}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.3208/} }
TY - JOUR AU - Nguyen, Nhan AU - Valette, Guillaume TI - Whitney stratifications and the continuity of local Lipschitz–Killing curvatures JO - Annales de l'Institut Fourier PY - 2018 SP - 2253 EP - 2276 VL - 68 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.3208/ DO - 10.5802/aif.3208 LA - en ID - AIF_2018__68_5_2253_0 ER -
%0 Journal Article %A Nguyen, Nhan %A Valette, Guillaume %T Whitney stratifications and the continuity of local Lipschitz–Killing curvatures %J Annales de l'Institut Fourier %D 2018 %P 2253-2276 %V 68 %N 5 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.3208/ %R 10.5802/aif.3208 %G en %F 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, Volume 68 (2018) no. 5, pp. 2253-2276. doi : 10.5802/aif.3208. http://www.numdam.org/articles/10.5802/aif.3208/
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