Geodesic
On bi-Lipschitz stability of families of functions
Journal of Singularities, Tome 6 (2012), pp. 179-198

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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.
DOI : 10.5427/jsing.2012.6n
Classification : 14P10, 57R45 
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     author = {Guillaume Valette},
     title = {On {bi-Lipschitz} stability of families of functions},
     journal = {Journal of Singularities},
     pages = {179--198},
     publisher = {mathdoc},
     volume = {6},
     year = {2012},
     doi = {10.5427/jsing.2012.6n},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2012.6n/}
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Guillaume Valette. On bi-Lipschitz stability of families of functions. Journal of Singularities, Tome 6 (2012), pp. 179-198. doi: 10.5427/jsing.2012.6n

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