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

Thilliez, Vincent

doi:10.1090/S0002-9939-05-08253-5

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

Proc. Amer. Math. Soc. 134 (2006), 1527-1536

DOI: https://doi.org/10.1090/S0002-9939-05-08253-5

Published electronically: 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 $X$ of some analytic map-germ having maximal rank on a dense subset of $X$. We obtain a result in terms of Łojasiewicz 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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