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On the motion of a curve by its binormal curvature

Jerrard, Robert L., Didier Smets (2015)

Journal of the European Mathematical Society

We propose a weak formulation for the binormal curvature flow of curves in 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.

On the multiplicity of eigenvalues of conformally covariant operators

Yaiza Canzani (2014)

Annales de l’institut Fourier

Let ( M , g ) be a compact Riemannian manifold and P g an elliptic, formally self-adjoint, conformally covariant operator of order m acting on smooth sections of a bundle over M . We prove that if P g has no rigid eigenspaces (see Definition 2.2), the set of functions f C ( M , ) for which P e f g has only simple non-zero eigenvalues is a residual set in C ( M , ) . As a consequence we prove that if P g has no rigid eigenspaces for a dense set of metrics, then all non-zero eigenvalues are simple for a residual set of metrics in the C -topology....

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