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Math Help - change of variable in a surface integral

  1. #1
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    change of variable in a surface integral

    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)
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    Re: change of variable in a surface integral

    nobody?
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