Tensorization of $p$-weak differentiable structures
Differential Geometry
2022-06-13 v1 Metric Geometry
Abstract
We consider -weak differentiable structures that were recently introduced by the first and last named authors, and prove that the product of -weak charts is a -weak chart. This implies that the product of two spaces with a -weak differentiable structure also admits a -weak differentiable structure. We make partial progress on the tensorization problem of Sobolev spaces by showing an isometric embedding result. Further, we establish tensorization when one of the factors is PI.
Cite
@article{arxiv.2206.05046,
title = {Tensorization of $p$-weak differentiable structures},
author = {Sylvester Eriksson-Bique and Tapio Rajala and Elefterios Soultanis},
journal= {arXiv preprint arXiv:2206.05046},
year = {2022}
}
Comments
27 pages. All comments are welcome