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arXiv · 2605.08309

Physical derivation of the coarea formula and an elementary proof via gradient flow

Shibo Liu
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Abstract

In this note, we derive an elementary version of the coarea formula by considering the mass of a solid body with density $g (x)$. Then we present an rigorous proof using the changing variable formula. To this end we construct the diffeomorphism $\Phi$ via the gradient flow and compute its Jacobian determinant via geometric method.

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Shibo Liu. 2026-05-08. Physical derivation of the coarea formula and an elementary proof via gradient flow. https://arxiv.org/abs/2605.08309

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