Timeline for Questions on smoothness of Riemann metrics
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Aug 1, 2022 at 13:01 | history | edited | Anton Petrunin | CC BY-SA 4.0 |
proved by Samuil Shefel (1979) and rediscovered by Dennis DeTurck and Jerry Kazdan (1981)
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| Apr 21, 2011 at 2:02 | comment | added | Deane Yang | I will make sure to cite Shefel from now on. | |
| Apr 21, 2011 at 1:35 | comment | added | Anton Petrunin | You should also take into account that in Soviet Union the time from submission to publication was about 5 years. | |
| Apr 20, 2011 at 17:17 | vote | accept | Andrew | ||
| Apr 20, 2011 at 16:41 | comment | added | Willie Wong | @Deane: looking at the MR, the results seems to be roughly comparable. The main lemma mentioned in the MR is equivalent to theorem 2.1 of DeTurck-Kazdan. And it looks like from the review of '79 you get an a priori estimate from the connection coefficients back up to the metric: Theorem 2 controls the regularity of the conformal map by the regularity of the conformal factor, compare that to Theorem 3.4 of DeTurck-Kazdan. So I would guess "roughly the same result, slightly earlier, not communicated well to the 'west' for the obvious reasons." | |
| Apr 20, 2011 at 16:00 | comment | added | Anton Petrunin | Well, I do not know what is done in DeTurck--Kazdan, but (1) is done by Shefel. | |
| Apr 20, 2011 at 15:54 | comment | added | Deane Yang | Anton, thanks. I'm still not sure which papers you're citing. Is it: "Smoothness of a conformal mapping of Riemannian spaces. (Russian) Sibirsk. Mat. Zh. 23 (1982), no. 1, 153–159, 222."? And how do his results compare to DeTurck and Kazdan? Did he prove the same results either earlier or independently? Or does he prove more? | |
| Apr 20, 2011 at 15:46 | history | edited | Anton Petrunin | CC BY-SA 3.0 |
deleted 24 characters in body
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| Apr 20, 2011 at 15:40 | comment | added | Anton Petrunin | @Deane: Shefel, S. Z. --- 1979 and 1982. both in Russian the second one is translated. | |
| Apr 20, 2011 at 15:21 | comment | added | Deane Yang | Anton, what's the reference for Shefel? | |
| Apr 20, 2011 at 15:16 | history | answered | Anton Petrunin | CC BY-SA 3.0 |