{"paper":{"title":"Reynolds Transport Theorem for Smooth Deformations of Currents on Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Lior Falach, Reuven Segev","submitted_at":"2013-12-30T10:17:00Z","abstract_excerpt":"The Reynolds transport theorem for the rate of change of an integral over an evolving domain is generalized. For a manifold $B$, a differentiable motion $m$ of $B$ in the manifold $\\mathcal{S}$, an $r$-current $T$ in $B$, and the sequence of images $m(t)_{\\sharp}T$ of the current under the motion, we consider the rate of change of the action of the images on a smooth $r$-form in $\\mathcal{S}$. The essence of the resulting computations is that the derivative operator is represented by the dual of the Lie derivative operation on smooth forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7671","kind":"arxiv","version":3},"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"}