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arXiv · 1512.03177

Sobolev spaces on warped products

Nicola Gigli·Bang-Xian Han
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Abstract

We study the structure of Sobolev spaces on the cartesian/warped products of a given metric measure space and an interval. Our main results are: - the characterization of the Sobolev spaces in such products - the proof that, under natural assumptions, the warped products possess the Sobolev-to-Lipschitz property, which is key for geometric applications. The results of this paper have been needed in the recent proof of the `volume-cone-to-metric-cone' property of ${\sf RCD}$ spaces obtained by the first author and De Philippis.

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Nicola Gigli, Bang-Xian Han. 2017-05-18. Sobolev spaces on warped products. https://arxiv.org/abs/1512.03177

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