Timeline for Behaviour of mass for currents with disjoint supports
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 13, 2020 at 17:55 | vote | accept | Eduardo Longa | ||
| Aug 13, 2020 at 17:54 | comment | added | Rohil Prasad | Oh, I wasn't very careful about that. I think my argument can be fixed to show that, by picking some two-form $\eta$ supported disjointly from $\chi\omega_k$ such that $\beta(\eta) > 0$. Then, if we assume $\alpha(\chi\omega_k) > 0$ for every $k$ as well, you get $\lim_{k \to \infty} |(\alpha + \beta)(\chi\omega_k + \eta)|$ is equal to $\lim_{k \to \infty} |\alpha(\chi\omega_k)| + |\beta(\eta)|$. This is strictly greater than $M(\alpha)$, but bounded above by $M(\alpha + \beta)$ which gives you the strict inequality. | |
| Aug 13, 2020 at 17:47 | comment | added | Eduardo Longa | Nice argument. In the particular case I described, the mass of $\alpha$ is stricly smaller than that of the sum, right? | |
| Aug 13, 2020 at 17:37 | history | answered | Rohil Prasad | CC BY-SA 4.0 |