Timeline for Estimate the gradient (with respect to local coordinates) of a partition of unity on a manifold
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 1 at 19:51 | comment | added | Anar C | You are very right! Thank you very much. | |
| Feb 27 at 21:59 | comment | added | Christian Remling | Not at all. What I'm saying is that whatever $\rho_n,\phi_n$ are for these $U_n$, it can never be true that $\rho'_n\le C\phi_n\le C$ for all $n$, for any $C$. | |
| Feb 27 at 18:29 | comment | added | Anar C | Christian, you seem to have examined the statement for a specific partition of unity, but my question asks for existence of not only the constant $C$, but also two sets of partition of unity, which, if exist, could be very different ones from the one you mentioned. | |
| Feb 26 at 15:17 | comment | added | Christian Remling | No. For example $M=\mathbb R$, $U_n=(\log n-2^{-n},\log (n+1)+2^{-n})$ (and other $U$'s that cover the negative part of $\mathbb R$). Then since $|U_n|\to 0$, you cannot keep $\rho'_n$ uniformly bounded. | |
| Feb 26 at 15:05 | history | asked | Anar C | CC BY-SA 4.0 |