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arXiv · 2403.07702

Lipschitz maps with prescribed local Lipschitz constants

Aidan Backus·Ng Ze-An
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Abstract

Let $\Gamma$ be a closed subset of a complete Riemannian manifold $M$ of dimension $\geq 2$, let $f: M \to N$ be a Lipschitz map to a complete Riemannian manifold $N$, and let $\psi$ be a continuous function which dominates the local Lipschitz constant of $f$. We construct a Lipschitz map which agress with $f$ on $\Gamma$ and whose local Lipschitz constant is $\psi$.

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Aidan Backus, Ng Ze-An. 2024-03-12. Lipschitz maps with prescribed local Lipschitz constants. https://arxiv.org/abs/2403.07702

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