The Invariant Symplectic Action and Decay for Vortices

Details The Invariant Symplectic Action and Decay for Vortices The Invariant Symplectic Action and Decay for Vortices

2006-11-24

arxiv.org/abs/math/0611768v5

Mathematics

Symplectic Geometry

20 pages. Final version. (I shortened the version # 3 a lot.) Accepted for publication by J. Symplectic Geom

Scientific paper

The (local) invariant symplectic action functional $\A$ is associated to a Hamiltonian action of a compact connected Lie group $\G$ on a symplectic manifold $(M,\omega)$, endowed with a $\G$-invariant Riemannian metric $<\cdot,\cdot>_M$. It is defined on the set of pairs of loops $(x,\xi):S^1\to M\x\Lie\G$ for which $x$ satisfies some admissibility condition. I prove a sharp isoperimetric inequality for $\A$ if $<\cdot,\cdot>_M$ is induced by some $\omega$-compatible and $\G$-invariant almost complex structure $J$, and, as an application, an optimal result about the decay at $\infty$ of symplectic vortices on the half-cylinder $[0,\infty)\x S^1$.

Affiliated with

Also associated with

No associations

Rating

The Invariant Symplectic Action and Decay for Vortices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Invariant Symplectic Action and Decay for Vortices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Invariant Symplectic Action and Decay for Vortices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-626790