The (local) invariant symplectic action functional is associated to a Hamiltonian action of a compact connected Lie group on a symplectic manifold (M,ω), endowed with a -invariant Riemannian metric <⋅,⋅>M. It is defined on the set of pairs of loops (x,ξ):S¹→ M for which x
Nearby in the stack
satisfies some admissibility condition. I prove a sharp isoperimetric inequality for
if
<⋅,⋅>M
is induced by some
ω
-compatible and
-invariant almost complex structure
J
, and, as an application, an optimal result about the decay at