{"paper":{"title":"Global analysis of the generalised Helfrich flow of closed curves immersed in $\\R^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Glen Wheeler","submitted_at":"2012-05-27T06:28:06Z","abstract_excerpt":"In this paper we consider the evolution of regular closed elastic curves $\\gamma$ immersed in $\\R^n$. Equipping the ambient Euclidean space with a vector field $\\ca:\\R^n\\rightarrow\\R^n$ and a function $f:\\R^n\\rightarrow\\R$, we assume the energy of $\\gamma$ is smallest when the curvature $\\k$ of $\\gamma$ is parallel to $\\c = (\\ca \\circ \\gamma) + (f \\circ \\gamma) \\tau$, where $\\tau$ is the unit vector field spanning the tangent bundle of $\\gamma$. This leads us to consider a generalisation of the Helfrich functional $\\SH$, defined as the sum of the integral of $|\\k-\\c|^2$ and $\\lambda$-weighted "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5939","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"}