{"paper":{"title":"Sobolev regularity of compactified 3-manifolds and the ADM Center of Mass","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math.AP"],"primary_cat":"math.DG","authors_text":"Rodrigo Avalos","submitted_at":"2024-03-06T20:24:51Z","abstract_excerpt":"In this paper, we address the existence of preferred asymptotic coordinates on asymptotically Euclidean (AE) manifolds $(M^3,g)$ such that $g$ admits an asymptotically Schwarzschildian first order expansion, based purely on a priori geometric conditions, which will then be used to establish geometric criteria guaranteeing the convergence of the ADM center of mass (COM). This question is analysed relating it to the study of the regularity of conformal compactifications of such manifolds, which is itself explored via elliptic theory for operators with coefficients of very limited regularity. Wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.04034","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.04034/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}