Rigidity of bi-Lipschitz equivalence of weighted homogeneous function-germs in the plane
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- by Alexandre Fernandes and Maria Ruas PDF
- Proc. Amer. Math. Soc. 141 (2013), 1125-1133 Request permission
Abstract:
The main goal of this work is to show that if two weighted homogeneous (but not homogeneous) function-germs $(\mathbb {C}^2,0)\rightarrow (\mathbb {C},0)$ 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.References
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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
- MR Author ID: 676391
- 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
- MR Author ID: 239264
- ORCID: 0000-0001-8890-524X
- Email: maasruas@icmc.usp.br
- Received by editor(s): February 22, 2011
- Received by editor(s) in revised form: June 30, 2011, and August 8, 2011
- Published electronically: August 20, 2012
- Communicated by: Lev Borisov
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 1125-1133
- MSC (2010): Primary 14B05; Secondary 14J17
- DOI: https://doi.org/10.1090/S0002-9939-2012-11388-7
- MathSciNet review: 3008860