{"paper":{"title":"Optimal paths for symmetric actions in the unitary group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.DG","authors_text":"Alejandro Varela, Gabriel Larotonda, Jorge Antezana","submitted_at":"2011-07-13T00:10:45Z","abstract_excerpt":"Given a positive and unitarily invariant Lagrangian L defined in the algebra of Hermitian matrices, and a fixed interval $[a,b]\\subset\\mathbb R$, we study the action defined in the Lie group of $n\\times n$ unitary matrices $\\mathcal{U}(n)$ by $$ S(\\alpha)=\\int_a^b L(\\dot\\alpha(t))\\,dt\\,, $$ where $\\alpha:[a,b]\\to\\mathcal{U}(n)$ is a rectifiable curve. We prove that the one-parameter subgroups of $\\mathcal{U}(n)$ are the optimal paths, provided the spectrum of the exponent is bounded by $\\pi$. Moreover, if L is strictly convex, we prove that one-parameter subgroups are the unique optimal curves"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2439","kind":"arxiv","version":1},"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"}