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Bi-Lipschitz \(\mathcal A \)-equivalence of \(\mathcal K \)-equivalent map-germs

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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas Aims and scope Submit manuscript

Abstract

In this paper, two sufficient conditions are provided for given two \(\mathcal K \)-equivalent map-germs to be bi-Lipschitz \(\mathcal A \)-equivalent. These are Lipschitz analogues of the known results on \(C^r\) \(\mathcal A \)-equivalence \((0\le r\le \infty )\) for given two \(\mathcal K \)-equivalent map-germs. As a corollary of one of our results, a Lipschitz version of the well-known Fukuda–Fukuda theorem is provided.

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Acknowledgments

The authors are grateful to the reviewers for careful reading of the first draft of their paper and giving important comments.

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Authors and Affiliations

  1. Departamento de Matemática, IBILCE-UNESP, Campus de São José do Rio Preto, SP, Brazil

    J. C. F. Costa

  2. Research Group of Mathematical Sciences, Research Institute of Environment and Information Sciences, Yokohama National University, Yokohama, 240-8501, Japan

    T. Nishimura

  3. Departamento de Matemática, Instituto de Ciéncias Matem’aticas e de Computacão, Universidade de São Paulo, Caixa Postal 668, São Carlos, SP, 13560-970 , Brazil

    M. A. S. Ruas

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  1. J. C. F. Costa
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  2. T. Nishimura
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  3. M. A. S. Ruas
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Correspondence to T. Nishimura.

Additional information

T. Nishimura was partially supported by JSPS and CAPES under the Japan–Brazil research cooperative program. The authors J.C.F. Costa and M.A.S. Ruas were partially supported by CNPq, CAPES and FAPESP.

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Costa, J.C.F., Nishimura, T. & Ruas, M.A.S. Bi-Lipschitz \(\mathcal A \)-equivalence of \(\mathcal K \)-equivalent map-germs. RACSAM 108, 173–182 (2014). https://doi.org/10.1007/s13398-012-0105-3

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  • DOI: https://doi.org/10.1007/s13398-012-0105-3

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