Rectifiable Curve


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rectifiable curve

[′rek·tə‚fī·ə·bəl ′kərv]
(mathematics)
A curve whose length can be computed and is finite.

Rectifiable Curve

 

a curve of finite length. The length of the curve is the limit of the sequence of lengths of polygonal lines inscribed in the curve such that the length of the longest line segment in the polygonal lines approaches zero. This limit always exists. It may, however, be infinite, in which case the curve is unrectifiable.

References in periodicals archive ?
It seems difficult to give interesting explicit examples of polynomial hulls of rectifiable curves, but we do have the following example: There is a rectifiable curve which is simple except for one self-intersection and whose hull has infinite genus.
Given a rectifiable curve [gamma] whose hull is a Riemann surface which is regular for the Dirichlet problem, we would like to say that harmonic measure for a point p [element of ] [gamma]\[gamma] is absolutely continuous with respect to arclength on [gamma]; furthermore, it would be natural to hope that harmonic measure be given by integration of the normal derivative of the Green's function with respect to arclength on [gamma].
Let [gamma] be a rectifiable curve such that [gamma]\[gamma] is a Riemann surface which is regular for the Dirichlet problem.