Hello. I was asking if there exists a change of variable formula for suraface integrals.

I know that if $\displaystyle \lambda$ is the Lebesgue measure in $\displaystyle R^n$ and $\displaystyle \phi$ is a diffeomorphism of open sets of $\displaystyle R^n$, I can write

$\displaystyle x=\phi(y)\Rightarrow\lambda(dx)=|detJac(\phi)(y)|\ \lambda(dy)$ .

But if I consider $\displaystyle \sigma$, the p-dimensional Hausdorff measure (p<n), and $\displaystyle \psi$ is a diffeomorphism of two p-manifolds of $\displaystyle R^n$, does it exist a similar formula? like

$\displaystyle x=\psi(y)\Rightarrow\sigma(dx)=??\ \sigma(dy)$