Proceedings of the American Mathematical Society

Infinite determinacy on a closed set for smooth germs with non-isolated singularities

Author(s): Vincent Thilliez
Journal: Proc. Amer. Math. Soc. 134 (2006), 1527-1536.
MSC (2000): Primary 58K40
Posted: October 13, 2005
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Abstract: We give necessary and sufficient conditions for infinite determinacy of a smooth function germ whose critical locus contains a given set. This set is assumed to be the zero variety

of some analytic map-germ having maximal rank on a dense subset of

. We obtain a result in terms of $\L$ ojasiewicz estimates which extends, in particular, previous works by Sun and Wilson on line singularities, and by Grandjean on singularities of codimension

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Vincent Thilliez
Affiliation: Mathématiques - Bâtiment M2, Université des Sciences et Technologies de Lille, F-59655 Villeneuve d'Ascq Cedex, France
Email: thilliez@math.univ-lille1.fr

DOI: 10.1090/S0002-9939-05-08253-5
PII: S 0002-9939(05)08253-5
Received by editor(s): December 13, 2004
Posted: October 13, 2005
Communicated by: Mei-Chi Shaw
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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ISSN 1088-6826 (e) ISSN 0002-9939 (p)

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