On bi-Lipschitz stability of families of functions

Guillaume Valette

Journal of Singularities
volume 6 (2012), 179-198
Proceedings of the Workshop on Singularities in Geometry and Applications, Będlewo, 5 – 21 May 2011

Received: 28 December 2011. Received in revised form: 28 March 2012.

DOI: 10.5427/jsing.2012.6n

Add a reference to this article to your citeulike library.


We focus on the Lipschitz stability of families of functions. We introduce a stability notion, called fiberwise bi-Lipschitz equivalence, which preserves the metric structure of the level surfaces of functions and show that it does not admit continuous moduli in the framework of semialgebraic geometry. We trivialize semialgebraic families of Lipschitz functions by constructing triangulations of their generic fibers which contain information about the metric structure of the sets.


Lipschitz triviality, semialgebraic functions, continuous moduli, triangulation of functions

Mathematical Subject Classification:

14P10, 57R45

Author(s) information:

Guillaume Valette
Instytut Matematyczny PAN
ul. Św. Tomasza 30
31-027 Kraków, Poland
email: gvalette@impan.pl