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Functions not constant on fractal quasi-arcs of critical points

Functions not constant on fractal quasi-arcs of critical points

This paper provides geometric sufficient conditions for an arc to be a critical set for some function not constant along that arcā€”an example of which was first discovered by Whitney in 1935. In particular, any fractal subarc of a quasi-circle has this property. The maximum degree of differentiability of the ā€¦