Uniqueness of the topological multivortex solution in the self-dual Chern-Simons theory

We establish a uniqueness result for the topological multivortex solution to the self-dual equations of the Abelian relativistic self-dual Chern-Simons-Higgs model. We prove that the topological multivortex solution is unique if the Chern-Simons coupling parameter κ>0 is sufficiently small. We also establish a uniqueness result for κ>0 sufficiently large