Smooth coarea formula
id:
smooth-coarea-formula-253-11472068
title:
Smooth coarea formula
text:
In Riemannian geometry, the smooth coarea formulas relate integrals over the domain of certain mappings with integrals over their codomains. Let M , N be smooth Riemannian manifolds of respective dimensions m ≥ n . Let F : M ⟶ N be a smooth surjection such that the pushforward (differential) of F is surjective almost everywhere. Let φ : M ⟶ [ 0 , ∞ ) a measurable function. Then, the following two equalities hold: where N J F is the normal Jacobian of F , i.e. the determinant of the derivative re
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wiki
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encyclopedia
description:
original url:
https://en.wikipedia.org/wiki/Smooth_coarea_formula
date created:
date modified:
2023-08-12T00:19:02Z
main entity:
{"identifier":"Q7546417","url":"https://www.wikidata.org/entity/Q7546417"}
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fields total:
13
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13