{"paper":{"title":"On conformal surfaces of annulus type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Yong Luo","submitted_at":"2011-10-24T21:21:02Z","abstract_excerpt":"Let $a>b>0$ and $f$ be a conformal map from $B_a\\setminus B_b\\subseteq R^2$ into $\\R^n$, with $|\\nabla f|^2=2e^{2u}$. Then $(e_1, e_2)$ with $e_1=e^{-u}\\frac{\\partial f}{\\partial r},$ and $e_2=r^{-1}e^{-u}\\frac{\\partial f}{\\partial\\theta}$ is a moving frame on $f(B_a\\setminus B_b)$. It satisfies the following equation $$d\\star<de_1, e_2>=0,$$ where $\\star$ is the Hodge star operator on $R^2$ with respect to the standard metric.\n  We will study the Dirichret energy of this frame and give some applications."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5357","kind":"arxiv","version":4},"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"}