Boundedness of Differential of Symplectic Vortices in Open Cylinder Model

Hai-Long Her ()
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Hai-Long Her: Department of Mathematics, Jinan University, Guangzhou 510632, China

Mathematics, 2024, vol. 12, issue 22, 1-12

Abstract: 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 .

Keywords: symplectic manifold; Hamiltonian action; moment map; symplectic vortex (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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