{"paper":{"title":"A topological lower bound for the energy of a unit vector field on a closed Euclidean hypersurface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Adriana V. Nicoli, Fabiano G. B. Brito, Icaro Gon\\c{c}alves","submitted_at":"2017-03-09T13:56:44Z","abstract_excerpt":"For a unit vector field on a closed immersed Euclidean hypersurface $M^{2n+1}$, $n\\geq 1$, we exhibit a nontrivial lower bound for its energy which depends on the degree of the Gauss map of the immersion. When the hypersurface is the unit sphere $\\mathbb{S}^{2n+1}$, immersed with degree one, this lower bound corresponds to a well established value from the literature. We introduce a list of functionals $\\mathcal{B}_k$ on a compact Riemannian manifold $M^{m}$, $1\\leq k\\leq m$, and show that, when the underlying manifold is a closed hypersurface, these functionals possess similar properties rega"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03263","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"}