We consider when it is possible to bound the Lipschitz constant a priori in a homotopy between Lipschitzmaps. If one wants uniform bounds, this is essentially a finiteness condition on homotopy. This contrasts strongly with the question of whether one can homotop the maps through Lipschitz maps. We also give an application to cobordism and discuss analogous isotopy questions.
CITATION STYLE
Ferry, S., & Weinberger, S. (2013). Quantitative algebraic topology and Lipschitz homotopy. Proceedings of the National Academy of Sciences of the United States of America, 110(48), 19246–19250. https://doi.org/10.1073/pnas.1208041110
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