{"paper":{"title":"Helfrich's Energy and Constrained Minimisation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Stephan Wojtowytsch","submitted_at":"2016-08-09T14:54:49Z","abstract_excerpt":"For every $g\\in\\mathbb{N}_0$ and $\\epsilon>0$, we construct a smooth genus $g$ surface embedded into the unit ball with area $8\\pi$ and Willmore energy smaller than $8\\pi + \\epsilon$. From this we deduce that a minimising sequence for Willmore's energy in the class of genus $g$ surfaces embedded in the unit ball with area $8\\pi$ converges to a doubly covered sphere for all $g\\in\\mathbb{N}_0$. We obtain the same result for certain Canham-Helfrich energies with $\\chi_K\\leq 0$ without genus constraint and show that Canham-Helfrich energies with $\\chi_K>0$ are not bounded from below in the class o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02823","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"}