In Riemannian geometry, the smooth coarea formulas relate integrals over the domain of certain mappings with integrals over their codomains. Let M , N {\displaystyle \scriptstyle M,\,N} be smooth Riemannian manifolds of respective dimensions m ≥ n {\displaystyle \scriptstyle m\,\geq \,n} .
In Riemannian geometry, the smooth coarea formulas relate integrals over the domain of certain mappings with integrals over their codomains. Let M , N {\displaystyle \scriptstyle M,\,N} be smooth Riemannian manifolds of respective dimensions m ≥ n {\displaystyle \scriptstyle m\,\geq \,n} .
Source: Wikipedia "Smooth coarea formula" · CC BY-SA 4.0
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