{"paper":{"title":"Parametrix for wave equations on a rough background I: regularity of the phase at initial time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.AP","authors_text":"Jeremie Szeftel","submitted_at":"2012-04-08T23:12:18Z","abstract_excerpt":"This is the first of a sequence of four papers \\cite{param1}, \\cite{param2}, \\cite{param3}, \\cite{param4} dedicated to the construction and the control of a parametrix to the homogeneous wave equation $\\square_{\\bf g} \\phi=0$, where ${\\bf g}$ is a rough metric satisfying the Einstein vacuum equations. Controlling such a parametrix as well as its error term when one only assumes $L^2$ bounds on the curvature tensor ${\\bf R}$ of ${\\bf g}$ is a major step of the proof of the bounded $L^2$ curvature conjecture proposed in \\cite{Kl:2000}, and solved jointly with S. Klainerman and I. Rodnianski in \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1768","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"}