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May 7, 2016 at 2:06 comment added Graham Cox @AlexDegtyarev I agree that a complete (if and only if) classification cannot be purely local, but still think a partial answer may be possible. For instance, in the one-dimensional case the boundary of $F(M) \subset \mathbb{R}$ just consists of the maximum and minimum values of $F$, so any critical point that is not a local extrema must be mapped to the interior.
May 6, 2016 at 17:24 comment added Alex Degtyarev This is obviously not a local property.
May 6, 2016 at 17:17 review First posts
May 6, 2016 at 17:24
May 6, 2016 at 17:13 history asked Graham Cox CC BY-SA 3.0