Timeline for parallel transport along $W^{1,2}$-curves
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 23, 2010 at 19:03 | answer | added | Richard Montgomery | timeline score: 4 | |
| Oct 20, 2010 at 14:37 | vote | accept | Orbicular | ||
| Oct 20, 2010 at 14:23 | comment | added | Deane Yang | Orbicular, OK. Also, Caratheodory's theorem doesn't seem relevant to me. | |
| Oct 20, 2010 at 14:04 | answer | added | Deane Yang | timeline score: 3 | |
| Oct 20, 2010 at 7:22 | comment | added | Orbicular | @Deane: If you post your comment as an answer, I'd be inclined to accept it as an answer. (In particular since the proof outline you described is essentially the proof in the reference - up to clever choosing of norms...) As an aside: I stumbled upon Caratheodory's existence theorem - is there a relation? | |
| Oct 19, 2010 at 20:49 | comment | added | Deane Yang | Since $W^{1,2} \subset C^0$ and (i) is a linear first ODE, the usual rewrite-as-integral-equation proof seems to work and is rather straightforward. I don't recall seeing this written down anywhere, but, if I'm correct on this, it's easy to verify and summarize. | |
| Oct 19, 2010 at 20:41 | comment | added | Orbicular | I know a 40 year old refence in German. There the authors claim the statement to be well-known (and still give a proof in the appendix). Hence I thought there might be an English reference as well (since I get the feeling - while reading the paper - that the statement is not original to the paper) | |
| Oct 19, 2010 at 20:33 | comment | added | Deane Yang | And you know how to prove it but would like a reference? | |
| Oct 19, 2010 at 20:29 | comment | added | Orbicular | @Deane: That's correct! | |
| Oct 19, 2010 at 20:28 | comment | added | Deane Yang | $W^{1,2}$ means one derivative in $L_2$? | |
| Oct 19, 2010 at 20:19 | history | asked | Orbicular | CC BY-SA 2.5 |