Lipschitz continuity of Lipschitz-Killing curvature densities at infinity

• Si Tiep Dinh ^[2] ; Nhan Nguyen ^[1]
  1. [1] FPT University

     FPT University

     Vietnam

     
  2. [2] International Centre of Research and Postgraduate Training in Mathematics, Institute of Mathematics, Hanoi, Vietnam
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 2, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01030-z
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• Referencias bibliográficas
  • Bernig, A., Bröcker, L.: Lipschitz-Killing invariants. Math. Nachr. 245, 5–25 (2002)
  • Bröcker, L., Kuppe, M.: Integral geometry of tame sets. Geom. Dedicata. 82, 285–323 (2000)
  • Brodersen, H., Trotman, D.: Whitney (b)-regularity is weaker than Kuo’s ratio test for real algebraic stratifications. Math. Scand. 45, 27–34...
  • Comte, G., Merle, M.: Équisingularité réelle. II. Invariants locaux et conditions de régularité. Ann. Sci. Éc. Norm. Supér. (4) 41, 221–269...
  • Coste, M.: An introduction to o-minimal geometry, Dip. Mat. Univ. Pisa, Dottorato di Ricerca in Matematica, Istituti Editoriali e Poligrafici...
  • D’Acunto, D.: Valeurs critiques asymptotiques d’une fonction définissable dans une structure o-minimale. Ann. Polon. Math. 75, 35–45 (2000)
  • Dinh, S.T., Kurdyka, K., Le Gal, O.: Łojasiewicz inequality on non-compact domains and singularities at infinity. Internat. J. Math. 24(8),...
  • Dinh, S.T., Pham, T.S.: Lipschitz continuity of tangent directions at infinity. Bull. Sci. Math. 182(27), 103223 (2023)
  • Dutertre, N.: A Gauss-Bonnet formula for closed semi-algebraic sets. Adv. Geom. 8, 33–51 (2008)
  • Dutertre, N.: Euler characteristic and Lipschitz-Killing curvatures of closed semi-algebraic sets. Geom. Dedicata. 158, 167–189 (2012)
  • Dutertre, N.: Stratified critical points on the real Milnor fibre and integral-geometric formulas. J. Singul. 13, 87–106 (2015)
  • Dutertre, N.: Lipschitz-Killing curvatures and polar images. Adv. Geom. 19, 205–230 (2019)
  • 13. Dutertre, N.: Principal kinematic formulas for germs of closed definable sets. Adv. Math. 399(54), 108251 (2022)
  • Dutertre, N., Grandjean, V.: Gauss-Kronecker curvature and equisingularity at infinity of definable families. Asian J. Math. 25, 815–839 (2021)
  • Dutertre, N., Grandjean, V.: Equisingularity of real families and Lipschitz-Killing curature densities at infinity. To appear in Ann. Inst,...
  • Fu, J.H.G.: Curvature measures of subanalytic sets. Amer. J. Math. 116, 819–880 (1994)
  • Grandjean, V.: On the total curvatures of a tame function. Bull. Braz. Math. Soc. (N.S.) 39, 515–535 (2008)
  • Grandjean, V.: Tame functions with strongly isolated singularities at infinity: a tame version of a Parusi ´nski’s theorem. Geom. Dedicata....
  • Ioffe, A.: A Sard theorem for tame set-valued mappings. J. Math. Anal. Appl. 335, 882–901 (2007)
  • Juniati, D., Trotman, D., Valette, G.: Lipschitz stratifications and generic wings. J. London Math. Soc. 2(68), 133–147 (2003)
  • Kurdyka, K., Orro, P., Simon, S.: Semialgebraic Sard theorem for generalized critical values. J. Differ. Geom. 56, 67–92 (2000)
  • Kurdyka, K., Raby, G.: Densité des ensembles sous-analytiques. Ann. Inst. Fourier (Grenoble) 39, 753–771 (1989)
  • Loi, T.L.: Whitney stratification of sets definable in the structure Rexp, in Singularities and differential equations (Warsaw,: vol. 33 of...
  • Grandjean, V.: Verdier and strict Thom stratifications in o-minimal structures. Illinois J. Math. 42, 347–356 (1998)
  • Loi, T.L.: Lecture 1: o-minimal structures, in The Japanese-Australian Workshop on Real and Complex Singularities—JARCS III, vol. 43 of Proc....
  • Nguyen, N.: Structure métrique et géométrie des ensembles définissables dans des structures o-minimales. Aix-Marseille Université, Thèse de...
  • Nguyen, N., Trivedi, S., Trotman, D.: A geometric proof of the existence of definable Whitney stratifications. Illinois J. Math. 58, 381–389...
  • Nguyen, N., Valette, G.: Whitney stratifications and the continuity of local Lipschitz-Killing curvatures. Ann. Inst. Fourier (Grenoble) 68,...
  • Rabier, P.J.: Ehresmann fibrations and Palais-Smale conditions for morphisms of Finsler manifolds. Ann. of Math. 2(146), 647–691 (1997)
  • van den Dries, L.: Tame topology and o-minimal structures. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge...
  • Verdier, J.-L.: Stratifications de Whitney et théorème de Bertini-Sard. Invent. Math. 36, 295–312 (1976)