{"paper":{"title":"Convergence to harmonic maps for the Landau-Lifshitz flows on two dimensional hyperbolic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lifeng Zhao, Ze Li","submitted_at":"2016-11-30T14:38:41Z","abstract_excerpt":"In this paper, we prove that the solution of the Landau-Lifshitz flow $u(t,x)$ from $\\mathbb{H}^2$ to $\\mathbb{H}^2$ converges to some harmonic map as $t\\to\\infty$. The essential observation is that although there exist infinite numbers of harmonic maps from $\\Bbb H^2$ to $\\Bbb H^2$, the heat flow initiated from $u(t,x)$ for any given $t>0$ converges to the same harmonic map as the heat flow initiated from $u(0,x)$. This observation enables us to construct a variant of Tao's caloric gauge to reduce the convergence to harmonic maps for the Landau-Lifshitz flow to the decay of the corresponding "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.10180","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"}