{"paper":{"title":"Global Stability of the Nontrivial Solutions to the Wave Map Problem from Kerr $|a|\\ll M$ to the Hyperbolic Plane under Axisymmetric Perturbations Preserving Angular Momentum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"John Stogin","submitted_at":"2016-10-13T01:56:36Z","abstract_excerpt":"This document proves global boundedness and decay for axisymmetric perturbations of a known solution to the wave map problem from a slowly rotating $|a|\\ll M$ Kerr spacetime to the hyperbolic plane. This problem is motivated by the general axisymmetric stability of Kerr conjecture and was first posed by Ionescu and Klainerman in [IK14]. Two particular developments in this paper, the treatment of terms near the axis of symmetry and the use of a decay hierarchy for energy estimates on uniformly spacelike hypersurfaces, can be used for a variety of similar problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03910","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"}