English

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

Classical Analysis and ODEs 2007-06-13 v2

Abstract

We give necessary and sufficient conditions of infinite determinacy for smooth function germs 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 & Wilson on line singularities, and by Grandjean on singularities of codimension 1 or 2.

Cite

@article{arxiv.math/0406259,
  title  = {Infinite determinacy on a closed set for smooth germs with non-isolated singularities},
  author = {Vincent Thilliez},
  journal= {arXiv preprint arXiv:math/0406259},
  year   = {2007}
}

Comments

9 pages, AMS-LaTeX - cosmetic changes

R2 v1 2026-07-22T17:06:38.569Z