ACTA issues

The difference in length of curves in ${\msbm R}^n$

Brittany Terese Fasy

Acta Sci. Math. (Szeged) 77:1-2(2011), 359-367

Abstract. We bound the difference in length of two curves in terms of their total curvatures and the Fréchet distance. The bound is independent of the dimension of the ambient Euclidean space, it improves upon a bound by Cohen-Steiner and Edelsbrunner, and it generalizes a result by Fáry and Chakerian.

AMS Subject Classification (1991): 14H50, 53A04, 26D15

Keyword(s): curves, Fréchet distance, inequalities, length, total curvature

Received September 6, 2010, and in revised form September 17, 2010. (Registered under 66/2010.)