Physical derivation of the coarea formula and an elementary proof via gradient flow
General Mathematics
2026-05-12 v1
Abstract
In this note, we derive an elementary version of the coarea formula by considering the mass of a solid body with density . Then we present an rigorous proof using the changing variable formula. To this end we construct the diffeomorphism via the gradient flow and compute its Jacobian determinant via geometric method.
Cite
@article{arxiv.2605.08309,
title = {Physical derivation of the coarea formula and an elementary proof via gradient flow},
author = {Shibo Liu},
journal= {arXiv preprint arXiv:2605.08309},
year = {2026}
}