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Then there is no quasi-harmonic spheres $u:\\mathbb{R}^n\\ra N$ such that $$\\lim_{r\\ra\\infty}r^ne^{-\\f{r^2}{4}}\\int_{|x|\\leq r}e^{-\\f{|x|^2}{4}}|\\nabla u|^2dx=0.$$ This generalizes a result of the first named author and X. Zhu (Calc. Var., 2009). Our method is essentially the Moser iteration and thus very simpl"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1010.2407","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-12T14:58:17Z","cross_cats_sorted":[],"title_canon_sha256":"d78d0bee72bf891c898911d83b2d95ce9a16b20f9b66e4839a159edbb3cb3bfc","abstract_canon_sha256":"1081d352e8c95259850006861486030ed6ec945918e869256499e571b61ee4e3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:28.067082Z","signature_b64":"yxKA8j0IkKzmMBvclO24nz0B4D/GT4RG3hJr4j6ayglUvBHf1yVGbeO/UdHQk0kL4JcoDSJyz3cxSzDXy9tcAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98bc13e89a1eb6956a2b929b5eabd86d78ad0b845844e72cf7a8d6622484513d","last_reissued_at":"2026-05-18T04:39:28.066443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:28.066443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonexistence of quasi-harmonic sphere with large energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jiayu Li, Yunyan Yang","submitted_at":"2010-10-12T14:58:17Z","abstract_excerpt":"Nonexistence of quasi-harmonic spheres is necessary for long time existence and convergence of harmonic map heat flows. Let $(N,h)$ be a complete noncompact Riemannian manifolds. Assume the universal covering of $(N,h)$ admits a nonnegative strictly convex function with polynomial growth. Then there is no quasi-harmonic spheres $u:\\mathbb{R}^n\\ra N$ such that $$\\lim_{r\\ra\\infty}r^ne^{-\\f{r^2}{4}}\\int_{|x|\\leq r}e^{-\\f{|x|^2}{4}}|\\nabla u|^2dx=0.$$ This generalizes a result of the first named author and X. Zhu (Calc. Var., 2009). 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