Boundedness of Differential of Symplectic Vortices in Open Cylinder Model.

Let G be a compact connected Lie group, (X , ω , μ) a Hamiltonian G-manifold with moment map μ , and Z a codimension-2 Hamiltonian G-submanifold of X. We study the boundedness of the differential of symplectic vortices (A , u) near Z, where A is a connection 1-form of a principal G-bundle P over a punctured Riemann surface Σ ˚ , and u is a G-equivariant map from P to an open cylinder model near Z. We show that if the total energy of a family of symplectic vortices on Σ ˚ ≅ [ 0 , + ∞) × S 1 is finite, then the A-twisted differential d A u (r , θ) is uniformly bounded for all (r , θ) ∈ [ 0 , + ∞) × S 1 . [ABSTRACT FROM AUTHOR]