{"paper":{"title":"Twist maps as energy minimisers in homotopy classes: symmetrisation and the coarea formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ali Taheri, Charles Morris","submitted_at":"2017-01-27T09:47:39Z","abstract_excerpt":"Let $\\X = \\X[a, b] = \\{x: a<|x|<b\\}\\subset \\R^n$ with $0<a<b<\\infty$ fixed be an open annulus and consider the energy functional, \\begin{equation*} {\\mathbb F} [u; \\X] = \\frac{1}{2} \\int_\\X \\frac{|\\nabla u|^2}{|u|^2} \\, dx, \\end{equation*} over the space of admissible incompressible Sobolev maps \\begin{equation*} {\\mathcal A}_\\phi(\\X) = \\bigg\\{ u \\in W^{1,2}(\\X, \\R^n) : \\det \\nabla u = 1 \\text{ {\\it a.e.} in $\\X$ and $u|_{\\partial \\X} = \\phi$} \\bigg\\}, \\end{equation*} where $\\phi$ is the identity map of $\\overline \\X$. Motivated by the earlier works \\cite{TA2, TA3} in this paper we examine the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07987","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"}