Intrinsic Cheeger energy for the intrinsically Lipschitz constants
Abstract
Recently, in the metric spaces, Le Donne and the author introduced the so-called intrinsically Lipschitz sections. The main aim of this note is to adapt Cheeger theory for the classical Lipschitz constants in our new context. More precisely, we define the intrinsic Cheeger energy from to where is a metric measure space and we characterize it in terms of a suitable notion of relaxed slope. In order to get this result, in more general context, we establish some properties of the intrinsically Lipschitz constants like the Leibniz formula, the product formula and the upper semicontinuity of the asymptotic intrinsically Lipschitz constant.
Keywords
Cite
@article{arxiv.2205.15851,
title = {Intrinsic Cheeger energy for the intrinsically Lipschitz constants},
author = {Daniela Di Donato},
journal= {arXiv preprint arXiv:2205.15851},
year = {2022}
}
Comments
We introduce the spaces L^p for the maps from Y to R^s in section 5. This is because when $X=R$ we get the trivial case (i.e. intrinsically Lipschitz sections are Lipschitz in the classical sense). We drop the section of vector space because it is not correct