In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition...In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.展开更多
Risler ＆ Trotman in 1997 proved that the multiplicity of an analytic function germ is left-right lipschitz invariant, which provided a partial answer to Zariski conjecture. In this note, based on the recent work of C...Risler ＆ Trotman in 1997 proved that the multiplicity of an analytic function germ is left-right lipschitz invariant, which provided a partial answer to Zariski conjecture. In this note, based on the recent work of Comte, Milman ＆ Trotman, we generalize the work of them to prove that the multiplicity of a C^∞ differentiable function germ is also left-right lipschitz invariant.展开更多
基金Supported by the National Nature Science Foundation of China(10671009,60534080,10871149)
文摘In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.
基金This work is supported by NNSFC under Grant Nos.10261002,10371047
文摘Risler ＆ Trotman in 1997 proved that the multiplicity of an analytic function germ is left-right lipschitz invariant, which provided a partial answer to Zariski conjecture. In this note, based on the recent work of Comte, Milman ＆ Trotman, we generalize the work of them to prove that the multiplicity of a C^∞ differentiable function germ is also left-right lipschitz invariant.
