Suppose $M$ is a smooth manifold and $N$ a smooth manifold with boundary, $F:M\to N$ a smooth map, if $F(p)\in \partial N$, can $dF_p:T_pM\to T_{F(p)}N$ be surjective?
2026-03-25 17:39:27.1774460367
Can $dF_p:T_pM\to T_{F(p)}N$ be surjective?
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If $F(p)\in \partial N$, then $dF_p:T_pM\to T_{F(p)}N$ is not surjective; if $dF_p:T_pM\to T_{F(p)}N$ is surjective, then $F(p)\notin \partial N$.