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arXiv · 2503.04390

Isometric Representation of Lipschitz-Free Spaces over Connected Orientable Riemannian Manifolds

Franz Luggin
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Abstract

We show that the Lipschitz-Free Space over a connected orientable $n$-di\-men\-sio\-nal Riemannian manifold $M$ is isometrically isomorphic to a quotient of $L^1(M,TM)$, the integrable sections of the tangent bundle $TM$, if $M$ is either complete or lies isometrically inside a complete manifold $N$. Two functions are deemed equivalent in this quotient space if their difference has distributional divergence zero. This quotient is the pre-annihilator of the exact essentially bounded currents, and if $M$ is simply connected, one may replace ``exact'' with ``closed'' currents.

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Franz Luggin. 2025-03-06. Isometric Representation of Lipschitz-Free Spaces over Connected Orientable Riemannian Manifolds. https://arxiv.org/abs/2503.04390

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