We propose a weak formulation for the binormal curvature flow of curves in . This formulation is sufficiently broad to consider integral currents as initial data, and sufficiently strong for the weak-strong uniqueness property to hold, as long as self-intersections do not occur. We also prove a global existence theorem in that framework.
Cite this article
Robert L. Jerrard, Didier Smets, On the motion of a curve by its binormal curvature. J. Eur. Math. Soc. 17 (2015), no. 6, pp. 1487–1515DOI 10.4171/JEMS/536