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Rigidity of bi-Lipschitz equivalence of weighted homogeneous function-germs in the plane
Authors:
Alexandre Fernandes and Maria Ruas
Journal:
Proc. Amer. Math. Soc. 141 (2013), 1125-1133
MSC (2010):
Primary 14B05; Secondary 14J17
Posted:
August 20, 2012
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Abstract: The main goal of this work is to show that if two weighted homogeneous (but not homogeneous) function-germs  are bi-Lipschitz equivalent, in the sense that these function-germs can be included in a strongly bi-Lipschitz trivial family of weighted homogeneous function-germs, then they are analytically equivalent.
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(2010b:14117), http://dx.doi.org/10.1090/S1061-0022-09-01067-X
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- Alexandre Fernandes and Maria Ruas. Bilipschitz determinacy of quasihomogeneous germs. Glasgow Math. J. 46 (2004), pp. 77-82. MR 2034833 (2005f:58076)
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- Jean-Pierre Henry and Adam Parusinski. Existence of moduli for bilipschitz equivalence of analytic functions. Compositio Math. 136 (2003), pp. 217-235. MR 1967391 (2004d:32037)
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- Satoshi Koike and Adam Parusinski. Equivalence relations for two variable real analytic function germs. J. Math. Soc. Japan (to appear).
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- Jean Martinet. Singularités des fonctions et applications différentiables. (French) Deuxième Édition Corrigée. Monografias de Matemática da PUC/RJ, no. 1 (1977). MR 0464292 (57:4225)
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Additional Information
Alexandre 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
Maria Ruas
Affiliation:
Instituto de Ciências Matemáticas e Computação, Av. Trabalhador São-carlense 400, Centro Caixa Postal: 668 CEP 13560-970, São Carlos SP, Brasil
Email:
maasruas@icmc.usp.br
DOI:
http://dx.doi.org/10.1090/S0002-9939-2012-11388-7
PII:
S 0002-9939(2012)11388-7
Keywords:
Bi-Lipschitz,
isolated complex singularity
Received by editor(s):
February 22, 2011
Received by editor(s) in revised form:
June 30, 2011, and August 8, 2011
Posted:
August 20, 2012
Communicated by:
Lev Borisov
Article copyright:
© Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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