{"paper":{"title":"Heat flows on hyperbolic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Marius Lemm, Vladimir Markovic","submitted_at":"2015-06-14T02:03:59Z","abstract_excerpt":"In this paper we develop new methods for studying the convergence problem for the heat flow on negatively curved spaces and prove that any quasiconformal map of the sphere $\\mathbb{S}^{n-1}$, $n\\geq 3$, can be extended to the $n$-dimensional hyperbolic space such that the heat flow starting with this extension converges to a quasi-isometric harmonic map. This implies the Schoen-Li-Wang conjecture that every quasiconformal map of $\\mathbb{S}^{n-1}$, $n\\geq 3$, can be extended to a harmonic quasi-isometry of the $n$-dimensional hyperbolic space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04345","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"}