A third-order dispersive flow for closed curves into Kähler manifolds

Details A third-order dispersive flow for closed curves into Kähler manifolds A third-order dispersive flow for closed curves into Kähler manifolds

2007-07-18

arxiv.org/abs/0707.2660v3

Mathematics

Analysis of PDEs

25pages, final version

Scientific paper

This paper is devoted to studying the initial value problem for a third-order
dispersive equation for closed curves into K\"ahler manifolds. This equation is
a geometric generalization of a two-sphere valued system modeling the motion of
vortex filament. We prove the local existence theorem by using geometric
analysis and classical energy method.

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