Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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

Author: Vincent Thilliez
Journal: Proc. Amer. Math. Soc. 134 (2006), 1527-1536
MSC (2000): Primary 58K40
Published electronically: October 13, 2005
MathSciNet review: 2199202
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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 $ X $ of some analytic map-germ having maximal rank on a dense subset of $ X $. We obtain a result in terms of \Lojasiewicz estimates which extends, in particular, previous works by Sun and Wilson on line singularities, and by Grandjean on singularities of codimension $ 1 $ or $ 2 $.

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Vincent Thilliez
Affiliation: Mathématiques - Bâtiment M2, Université des Sciences et Technologies de Lille, F-59655 Villeneuve d’Ascq Cedex, France

Received by editor(s): December 13, 2004
Published electronically: October 13, 2005
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.