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Oct 11, 2019 at 9:40 comment added Stadionok This is what I guess too but it is not clear to me, how to adapt your proof...
Oct 10, 2019 at 13:43 comment added Mohammad Ghomi @Stadionok: I think that it should be possible to get $C^\infty$ ones, without giving up $C^1$-closeness.
Oct 10, 2019 at 6:14 comment added Stadionok Thank you for the reference! In this paper, the approximating curves are of class $C^2$ and I wonder if one could get $C^\infty$ ones (maybe at the expense of giving up $C^1$-closeness).
Oct 9, 2019 at 21:09 history answered Mohammad Ghomi CC BY-SA 4.0