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- Smooth_coarea_formula abstract "In Riemannian geometry, the smooth coarea formulas relate integrals over the domain of certain mappings with integrals over their codomains.Let be smooth Riemannian manifolds of respective dimensions . Let be a smooth surjection such that the pushforward (differential) of is surjective almost everywhere. Let a measurable function. Then, the following two equalities hold:where is the normal Jacobian of , i.e. the determinant of the derivative restricted to the orthogonal complement of its kernel.Note that from Sard's lemma almost every point is a regular point of and hence the set is a Riemannian submanifold of , so the integrals in the right-hand side of the formulas above make sense.".
- Smooth_coarea_formula wikiPageID "13373259".
- Smooth_coarea_formula wikiPageRevisionID "604515211".
- Smooth_coarea_formula hasPhotoCollection Smooth_coarea_formula.
- Smooth_coarea_formula subject Category:Riemannian_geometry.
- Smooth_coarea_formula comment "In Riemannian geometry, the smooth coarea formulas relate integrals over the domain of certain mappings with integrals over their codomains.Let be smooth Riemannian manifolds of respective dimensions . Let be a smooth surjection such that the pushforward (differential) of is surjective almost everywhere. Let a measurable function. Then, the following two equalities hold:where is the normal Jacobian of , i.e.".
- Smooth_coarea_formula label "Smooth coarea formula".
- Smooth_coarea_formula sameAs m.03c36pt.
- Smooth_coarea_formula sameAs Q7546417.
- Smooth_coarea_formula sameAs Q7546417.
- Smooth_coarea_formula wasDerivedFrom Smooth_coarea_formula?oldid=604515211.
- Smooth_coarea_formula isPrimaryTopicOf Smooth_coarea_formula.