Let R" be n-dimensional Euclidean space, and let c~: [0, L] -~ R" and fl: [0, L] -, ~" be closed rectifiable arcs in N" of the same total length L which are parametrized via their arc length. fl is said to be a chord-stretched version of • if for each 0 ~< s ~< t ~< L, Is(t)-e(s)l ~< Ifl(t) -fl(s)l, fl is said to be convex if fl is simple and if fl([0, L]) is the frontier of some plane convex set. Individual work by Professors G. Choquet and G. T. Sallee demonstrated that if ~ were simple then there existed a convex chord-stretched version fl of e. This result led Professor Yang Lu to conjecture that if ct were convex and fl were a chord-stretched version of ct then ~ and fl would be congruent, i.e. any chord-stretching map of a convex arc is an isometry. Professor Yang Lu has proved this conjecture in the case where c~ and ~ are C 2 curves. In this paper we prove the conjecture in general.

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