The total absolute torsion of open curves in $E^{3}$

Abstract

The total absolute torsion of smooth curves in $E^{3}$ is defined as the total integral of the absolute value of the torsion. This notion is extended to piecewise smooth curves. We study the infimum of the total absolute torsion in a certain set of curves, where the endpoints, the osculating planes at the endpoints and the length are all prescribed. We show how the infimum is calculated from the boundary data.