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On the motion of a curve by its binormal curvature. (English) Zbl 1327.53086
This paper is dedicated to the study of the binormal curvature flow of curves in $$\mathbb{R}^{3}$$. The authors have considered weak binormal curvature flows for finite mass currents. The paper consists of 5 parts, each of them very interesting. In Section 5, the authors have presented some examples and open questions but also some graphical results for the theory developed all over the paper.

##### MSC:
 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) 76B47 Vortex flows for incompressible inviscid fluids
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##### References:
 [1] Allard, W. K.: On the first variation of a varifold. Ann. of Math. (2) 95, 417-491 (1972) · Zbl 0252.49028 · doi:10.2307/1970868 [2] Almgren, F. J.: The Theory of Varifolds: A Variational Calculus in the Large for the k- dimensional Area Integrand. Institute for Advanced Study, Princeton (1964) (mimeographed notes)
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