Timeline for Can every diffeomorphism be rescaled into a volume preserving one?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jan 1, 2023 at 22:10 | answer | added | Anton Petrunin | timeline score: 2 | |
| Mar 28, 2020 at 6:23 | history | edited | Asaf Shachar | CC BY-SA 4.0 |
I have cleaned up the question and pointed on a purely PDE-type subquestion.
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| Mar 26, 2020 at 18:50 | comment | added | Asaf Shachar | @AlexArvanitakis Hi, I don't follow your reduction. Why is the question equivalent to finding a function $h$ such that $ \omega=h (f^\star\omega)$? According to my calculation, $(hf)^*\omega \neq h (f^\star\omega)$. I also don't see the connection to Moser's theorem. If you could elaborate that would be great. | |
| Mar 26, 2020 at 16:50 | comment | added | AlexArvanitakis | Surely yes? Pull the volume form $\omega$ back through $f$. $f^\star \omega$ is another volume form. Then the question is, does there exist $h$ so $\omega=h (f^\star\omega)$ which presumably can be shown to be true. Moser's theorem? | |
| Mar 26, 2020 at 16:01 | comment | added | Asaf Shachar | @YCor I meant for the standard (scalar) multiplication of a vector by a scalar. Your are right that the title was a bit misleading. I have edited the question to address this, and also clarified what do I mean by $h \cdot f$. Thanks for your comment. | |
| Mar 26, 2020 at 15:59 | history | edited | Asaf Shachar | CC BY-SA 4.0 |
added 131 characters in body; edited title
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| Mar 26, 2020 at 15:36 | comment | added | YCor | What is meant by $h\cdot f$? (I'd read it a priori as $h\circ f$, but then the question would be trivial taking $h=f^{-1}$). Where does "conformally" intervene in the question? If I were reading the title, I'd interpret it as whether for each $f$ there exists $h$ conformal such that $h\circ f\circ h^{-1}$ is area-preserving. | |
| Mar 26, 2020 at 15:28 | history | asked | Asaf Shachar | CC BY-SA 4.0 |