Timeline for Defining surface integral on boundary of $C^1$-domain
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Jan 23, 2014 at 10:24 | vote | accept | michael_carbon | ||
| Jan 13, 2014 at 13:13 | comment | added | Ben McKay | The chart function is a diffeomorphism, which suffices. You can take any oriented orthonormal basis of the tangent space of $\partial \Omega$ at a point, and wedge it together to give a volume form. That is the volume form whose associated measure we want to integrate, and that is the volume form whose integrals agree with the integrals I have described by extending functions to be constant in perpendicular directions. | |
| Jan 12, 2014 at 11:47 | comment | added | michael_carbon | Thanks for answering. "..recovers the usual Lebesgue integral on $\partial\Omega$, by taking charts." -- this usual integral by taking charts does not require an affine transformation of coordinates, right? The chart function is a diffeomorphism which suffices. | |
| Jan 11, 2014 at 17:58 | history | answered | Ben McKay | CC BY-SA 3.0 |