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Thread: 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 $\displaystyle \lambda$ 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
    $\displaystyle x=\psi(y)\Rightarrow\sigma(dx)=??\ \sigma(dy)$
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    Re: change of variable in a surface integral

    nobody?
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