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Lipschitz maps with prescribed local Lipschitz constants

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arxiv 2403.07702 v1 pith:S2W3P6FQ submitted 2024-03-12 math.DG math.CA

Aidan Backus , Ng Ze-An This is my paper · ORCID
classification math.DGmath.CA
keywords lipschitzlocalcompleteconstantgammamanifoldriemannianagress
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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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    Each unit costable cohomology class on a closed oriented Riemannian d-manifold (2 to 7) determines a unique largest lamination of minimal hypersurfaces calibrated by every calibration in the class, constraining the st...

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