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Lipschitz classification of functions on a Hölder triangle

Author(s): L. Birbrair; A. Fernandes; D. Panazzolo
Original publication: Algebra i Analiz, tom 20 (2008), nomer 5.
Journal: St. Petersburg Math. J. 20 (2009), 681-686.
MSC (2000): Primary 32S15, 32S05
Posted: July 21, 2009
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Abstract: The problem of semialgebraic Lipschitz classification of quasihomogeneous polynomials on a Hölder triangle is studied. For this problem, the ``moduli'' are described completely in certain combinatorial terms.

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L. Birbrair, Local bi-Lipschitz classification of $ 2$-dimensional semialgebraic sets, Houston J. Math. 25 (1999), no. 3, 453-472. MR 1730886 (2000j:14091)

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R. Benedetti and M. Shiota, Finiteness of semialgebraic types of polynomial functions, Math. Z. 208 (1991), no. 4, 589-596. MR 1136477 (92j:14068)

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L. Birbrair, J. Costa, A. Fernandes, and M. Ruas, $ \mathcal{K}$-bi-Lipschitz equivalence of real function-germs, Proc. Amer. Math. Soc. 135 (2007), no. 4, 1089-1095. MR 2262910 (2007m:58048)

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T. Fukuda, Types topologiques des polynômes, Inst. Hautes Études Sci. Publ. Math. No. 46 (1976), 87-106. MR 0494152 (58:13080)

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J.-P. Henry and A. Parusinski, Existence of moduli for bi-Lipschitz equivalence of analytic functions, Compositio Math. 136 (2003), no. 2, 217-235. MR 1967391 (2004d:32037)

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T. Mostowski, Lipschitz equisingularity, Dissertationes Math. 243 (1985), 46 pp. MR 0808226 (87e:32008)

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Additional Information:

L. Birbrair
Affiliation: Departamento de Matemática, Universidade Federal do Ceará, Av. Mister Hull s/n, Campus do PICI, Bloco 914, CEP: 60.455-760 - Fortaleza - CE, Brasil
Email: birb@ufc.br

A. Fernandes
Affiliation: Departamento de Matemática, Universidade Federal do Ceará, Av. Mister Hull s/n, Campus do PICI, Bloco 914, CEP: 60.455-760 - Fortaleza - CE, Brasil
Email: alexandre.fernandes@ufc.br

D. Panazzolo
Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-090 - São Paulo - SP, Brazil
Email: dpanazzo@ime.usp.br

DOI: 10.1090/S1061-0022-09-01067-X
PII: S 1061-0022(09)01067-X
Keywords: Lipschitz classification, quasihomogeneous polynomials, H\"older triangle, moduli
Received by editor(s): 16/APR/2007
Posted: July 21, 2009
Additional Notes: The first author was supported by CNPq grant 300985/93-2. The second author was supported by CNPq grant 300393/2005-9, and also by CNPq/FUNCAP/PPP. The third author was supported by CNPq grant 305904/2003-5.
Copyright of article: Copyright 2009, American Mathematical Society

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