Taking $S$ a smooth surface, $\omega$ a 1-form with compact support that is exact ie $\omega=df$ with $f\in\mathscr{C}^\infty(S)$. Is it always possible to have $f$ with compact support?
2026-04-04 13:41:06.1775310066
$\omega=df$ with $\omega$ compact supported: $f$ compact supported possible?
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