Timeline for "Constrained" Moser's Trick
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 5 at 14:06 | comment | added | Moishe Kohan | I did not check details but what you should do is to compare the ODEs of evolution of outer and inner-directed normal vector fields for an edge $e$ (coming from the flows on the adjacent faces). Check if they match. | |
| Oct 5 at 13:41 | comment | added | Mirko | @MoisheKohan I'm reading trhough the linked papare, but still I don't see how to get at least $C^1$ so easily... | |
| Oct 3 at 17:15 | comment | added | Mirko | @moisheKohan Yea, I:ve just noticed that there is subtle issue about the smoothness of the map one obtains | |
| Oct 3 at 16:44 | comment | added | Moishe Kohan | Also, you should be careful about the degree of smoothness of the diffeomorphism, as far as I can tell, you get $C^0$ for free, get $C^1$ relatively easily, but to get $C^\infty$ you need more work. | |
| Oct 3 at 16:40 | comment | added | Mirko | @MoisheKohan and regarding that assumption, luckily I have it. For the background I'm working with $\omega(0) = dx\wedge dy$ | |
| Oct 3 at 16:26 | comment | added | Mirko | @MoishaKohan I'll look into it. If that does the job, you have just saved my master graduation this month, and hence my phd admission | |
| Oct 3 at 15:32 | comment | added | Moishe Kohan | This is a special case of Moser's theorem for manifolds with corners, arxiv.org/abs/1604.07787, under a mild assumption about values of the area forms at the vertex points (they should coincide). To treat the general case, you should read their proof and try to adapt it to your setting. | |
| Oct 3 at 15:05 | comment | added | Mirko | And if we suppose that $G$ is a tree? | |
| Oct 3 at 14:25 | comment | added | Ben McKay | The areas of planar regions cut out by $G$ surely have to be the same for both area forms. | |
| Oct 3 at 14:00 | history | edited | Mirko | CC BY-SA 4.0 |
deleted 2 characters in body
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| S Oct 3 at 13:53 | review | First questions | |||
| Oct 3 at 16:18 | |||||
| S Oct 3 at 13:53 | history | asked | Mirko | CC BY-SA 4.0 |