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arXiv · 2609.17034

On Strong Bi-Lipschitz Triviality of Deformations

Debomita Chakraborty·Saurabh Trivedi
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Abstract

The Thom-Levine theorem is a classical method for proving the triviality of deformations by integrating suitable vector fields. In this note, we show that the converse of this criterion does not hold in the bi-Lipschitz category. More precisely, we give an example of a smooth one-parameter deformation of a real function germ in two variables which is bi-Lipschitz trivial but not strongly bi-Lipschitz trivial. The central germ has an isolated critical point, though it is not finitely determined.

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Debomita Chakraborty, Saurabh Trivedi. 2026-09-15. On Strong Bi-Lipschitz Triviality of Deformations. https://arxiv.org/abs/2609.17034

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