On the motion of a curve by its binormal curvature

By Robert L. Jerrard, D. Smets. 2011

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We propose a weak formulation for the binormal curvature flow of curves in $\R^3.$ 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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9b379a82f8d16cdc14bde38cfd5b4a4a8a04ed8c