Calculus of Variations and Geometric Measure Theory
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N. Gigli - B. Han

Sobolev Spaces on Warped Products

created by gigli on 10 Dec 2015
modified on 18 May 2017


Submitted Paper

Inserted: 10 dec 2015
Last Updated: 18 may 2017

Year: 2015

With respect to the previous version, we improved the presentation and corrected few typos


We study the structure of Sobolev spaces on the cartesian and 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 RCD spaces obtained by the first author and De Philippis.


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