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Interaction energy between vortices of vector fields on Riemannian surfaces

Banff International Research Station for Mathematical Innovation and Discovery

We study a variational Ginzburg-Landau type model depending on a small parameter $\epsilon>0$ for (tangent) vector fields on a $2$-dimensional Riemannian surface. As $\epsilon\to 0$, the vector fields tend to be of unit length and will have singular points of a (non-zero) index, called vortices. Our main result determines the interaction energy between these vortices as a $\Gamma$-limit (at the second order) as $\epsilon\to 0$. We also prove similar results for problems involving vector fields on compact surfaces embedded in $\mathbb R^3$. This is joint work with Radu Ignat.

Mathematics; Partial differential equations; Statistical mechanics, structure of matter

video/mp4

Author affiliation: University of Toronto

2017-10-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63478

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/