Lipschitz classification of functions on a Hölder triangle

Birbrair, L.; Fernandes, A.; Panazzolo, D.

doi:10.1090/S1061-0022-09-01067-X

Lipschitz classification of functions on a Hölder triangle
HTML articles powered by AMS MathViewer

by L. Birbrair, A. Fernandes and D. Panazzolo

St. Petersburg Math. J. 20 (2009), 681-686

DOI: https://doi.org/10.1090/S1061-0022-09-01067-X

Published electronically: July 21, 2009

PDF | Request permission

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.

References

L. Birbrair, Local bi-Lipschitz classification of $2$-dimensional semialgebraic sets, Houston J. Math. 25 (1999), no. 3, 453–472. MR 1730886
Riccardo Benedetti and Masahiro Shiota, Finiteness of semialgebraic types of polynomial functions, Math. Z. 208 (1991), no. 4, 589–596. MR 1136477, DOI 10.1007/BF02571547
L. Birbrair, J. C. F. Costa, A. Fernandes, and M. A. S. Ruas, $\scr K$-bi-Lipschitz equivalence of real function-germs, Proc. Amer. Math. Soc. 135 (2007), no. 4, 1089–1095. MR 2262910, DOI 10.1090/S0002-9939-06-08566-2
Takuo Fukuda, Types topologiques des polynômes, Inst. Hautes Études Sci. Publ. Math. 46 (1976), 87–106 (French). MR 494152
Jean-Pierre Henry and Adam Parusiński, Existence of moduli for bi-Lipschitz equivalence of analytic functions, Compositio Math. 136 (2003), no. 2, 217–235. MR 1967391, DOI 10.1023/A:1022726806349
Tadeusz Mostowski, Lipschitz equisingularity, Dissertationes Math. (Rozprawy Mat.) 243 (1985), 46. MR 808226
Guillaume Valette, A bilipschitz version of Hardt’s theorem, C. R. Math. Acad. Sci. Paris 340 (2005), no. 12, 895–900 (English, with English and French summaries). MR 2152275, DOI 10.1016/j.crma.2005.05.004