One-vortex moduli space and Ricci flow
arXiv:0805.0211 · doi:10.1016/j.geomphys.2008.08.005
Abstract
The metric on the moduli space of one abelian Higgs vortex on a surface has a natural geometrical evolution as the Bradlow parameter, which determines the vortex size, varies. It is shown by various arguments, and by calculations in special cases, that this geometrical flow has many similarities to Ricci flow.
20 pages
References in corpus (6)
- Volume of Vortex Moduli Spaces
- Towards physically motivated proofs of the Poincare' and geometrization conjectures
- The dynamics of vortices on S^2 near the Bradlow limit
- Expansion for the solutions of the Bogomolny equations on the torus
- Vortices and Flat Connections
- Dynamics of critical vortices on the torus and on the plane
Cited by in corpus (7)
- On the L^2-metric of vortex moduli spaces
- Vortex Motion on Surfaces of Small Curvature
- Vortices and Jacobian varieties
- Higher Winding Strings and Confined Monopoles in N=2 SQCD
- Higher order geometric flows on three dimensional locally homogeneous spaces
- Ricci flows on surfaces related to the Einstein Weyl and Abelian vortex equations
- Bergman kernel on Riemann surfaces and Kaehler metric on symmetric products