Functions not constant on fractal quasi-arcs of critical points
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- by Alec Norton PDF
- Proc. Amer. Math. Soc. 106 (1989), 397-405 Request permission
Abstract:
This paper provides geometric sufficient conditions for an arc to be a critical set for some function not constant along that arc—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 function is closely connected to the arc’s geometry.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 106 (1989), 397-405
- MSC: Primary 28A75; Secondary 26B35, 58C25
- DOI: https://doi.org/10.1090/S0002-9939-1989-0969524-8
- MathSciNet review: 969524