I wonder if you could recommend a chapter or a paper on Stokes theorem for manifolds with corners.

I've found one here http://math.stanford.edu/~conrad/diffgeomPage/handouts.html (the third one from the bottom).

The statement is:

Let $(M, \mu)$ be an oriented manifold with corners and with constant dimension $n \ge 1$. Choose a compactly supported $\omega \in \Omega_{n-1}(M)$ and give $\partial (M_{\le 1})$ the induuced orientation $\partial \mu$ as the boundary of the manifold-with-boundary $M_{n \le 1}$. Then $\omega$ is absolutely integrable on $\partial (M_{\le 1})$ and $\int_{M} d \omega = \int_{\partial M_{\le 1}} \omega$

But while proving the theorem, the author explains how to prove the theorem above copying the proof of the Stokes theorem for manifolds with boundary and the problem is that I cannot find that proof on his website.

Do you know any other papers or books where (maybe other version of ) the theorem is proved?

  • 3
    $\begingroup$ See also Lang's Real Analysis. My edition is 1969. In the very last section he treats Stokes's Theorem with singularities. $\endgroup$ – Ted Shifrin Mar 12 '15 at 14:42

If you are looking for reference that specifically deals with Stokes' formula on manifolds with corners, John M. Lee's Introduction to Smooth Manifold, Second Edition, page 415-419 treats the case.


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