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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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