PreprintCC BY 4.0arXiv
Differentiability of Lipschitz mappings into metric spaces: area and co-area formulas
Abstract
We give a self-contained exposition of metric differentiability for Lipschitz mappings from sets in Euclidean spaces into arbitrary metric spaces, together with the corresponding area and co-area formulas. The novelty is a new metric implicit function theorem for mappings into metric spaces, which is then used to give a direct and geometric proof of the co-area formula for Lipschitz mappings into metric spaces.
Related
- Lipschitz numbers and fine differentiability on metric measure spaces
- Embeddability and rectifiability of Lipschitz differentiability spaces
- Differentiability of Lipschitz curves in p-Banach spaces
- Common Fixed Points of Co-Cyclic and Sub-Cyclic Mappings in Complete Metric Spaces
- Isometric copies of ℓ∞n in Lipschitz-free spaces over finite metric spaces
BibTeX
@misc{esmayli2026differentiability,
title = {{Differentiability of Lipschitz mappings into metric spaces: area and co-area formulas}},
author = {Behnam Esmayli and Paweł Goldstein and Piotr Hajłasz},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09121},
eprint = {2609.09121},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09121},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Differentiability of Lipschitz mappings into metric spaces: area and co-area formulas
AU - Behnam Esmayli
AU - Paweł Goldstein
AU - Piotr Hajłasz
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09121
UR - https://arxiv.org/abs/2609.09121
AB - We give a self-contained exposition of metric differentiability for Lipschitz mappings from sets in Euclidean spaces into arbitrary metric spaces, together with the corresponding area and co-area formulas. The novelty is a new metric implicit function theorem for mappings into metric spaces, which is then used to give a direct and geometric proof of the co-area formula for Lipschitz mappings into metric spaces.
ER -