On the multiplicity of a \(C^{\infty }\)-differentiable function-germ (Q2641534)
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| Language | Label | Description | Also known as |
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| English | On the multiplicity of a \(C^{\infty }\)-differentiable function-germ |
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On the multiplicity of a \(C^{\infty }\)-differentiable function-germ (English)
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20 August 2007
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\textit{J. Risler} and \textit{D. Trotman} [Bull. Lond. Math. Soc. 29, 200--204 (1997; Zbl 0892.32024)] proved that the multiplicity of an analytic function germ is left-right Lipschitz invariant, providing a partial answer to the Zariski conjecture. In this note, using the results of \textit{G. Comte, P. Milman} and \textit{D. Trotman} [Proc. Am. Math. Soc. 130, No.~7, 2045--2048 (2002; Zbl 0997.32022)] the author proves that the multiplicity of a smooth function germ is also left-right Lipschitz invariant.
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smooth function germ
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multiplicity
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bi-Lipschitz maps
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