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- W2953143670 abstract "Here a new notion of fractional length of a smooth curve, which depends on a parameter $sigma$, is introduced that is analogous to the fractional perimeter functional of sets that has been studied in recent years. It is shown that in an appropriate limit the fractional length converges to the traditional notion of length up to a multiplicative constant. Since a curve that connects two points of minimal length must have zero curvature, the Euler--Lagrange equation associated with the fractional length is used to motivate a nonlocal notion of curvature for a curve. This is analogous to how the fractional perimeter has been used to define a nonlocal mean curvature." @default.
- W2953143670 created "2019-06-27" @default.
- W2953143670 creator A5010301614 @default.
- W2953143670 date "2018-08-27" @default.
- W2953143670 modified "2023-09-27" @default.
- W2953143670 title "A fractional notion of length and an associated nonlocal curvature" @default.
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