{"paper":{"title":"Radially Symmetric Solutions To The Graphic Willmore Surface Equation","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jingyi Chen, Yuxiang Li","submitted_at":"2014-10-21T06:12:32Z","abstract_excerpt":"We show that a smooth radially symmetric solution $u$ to the graphic Willmore surface equation is either a constant or the defining function of a half sphere in ${\\mathbb R}^3$. In particular, radially symmetric entire Willmore graphs in ${\\mathbb R}^3$ must be flat. When $u$ is a smooth radial solution over a punctured disk $D(\\rho)\\backslash\\{0\\}$ and is in $C^1(D(\\rho))$, we show that there exist a constant $\\lambda$ and a function $\\beta$ in $C^0(D(\\rho))$ such that $u''(r) =\\frac{\\lambda}{2}\\log r+\\beta(r)$; moreover, the graph of $u$ is contained in a graphical region of an inverted cate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5547","kind":"arxiv","version":2},"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"}