change of variable in a surface integral

**qwertyuio** · August 27th 2011, 12:00 PM

Hello. I was asking if there exists a change of variable formula for suraface integrals.
I know that if $\lambda$ is the Lebesgue measure in $R^n$ and $\phi$ is a diffeomorphism of open sets of $R^n$ , I can write
$x=\phi(y)\Rightarrow\lambda(dx)=|detJac(\phi)(y)|\ \lambda(dy)$ .
But if I consider $\sigma$ , the p-dimensional Hausdorff measure (p<n), and $\psi$ is a diffeomorphism of two p-manifolds of $R^n$ , does it exist a similar formula? like
$x=\psi(y)\Rightarrow\sigma(dx)=??\ \sigma(dy)$

**qwertyuio** · August 31st 2011, 10:43 AM

nobody?

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