{"paper":{"title":"The Invariant Symplectic Action and Decay for Vortices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SG","authors_text":"Fabian Ziltener","submitted_at":"2006-11-24T20:42:06Z","abstract_excerpt":"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 symple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611768","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}