On Moving Ginzburg-Landau Vortices

In this note, we establish a quantization property for the heat equation of Ginzburg-Landau functional in R4 which models moving vortices of surface types. It asserts that if the energy is sufficiently small on a parabolic ball in R4 x R+ then there is no vortice in the parabolic ball of 1/2 radius. This extends a recent result of Lin-Riviere [LR3] in R3.

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Published 1 January 2004