{"paper":{"title":"The raising steps method. Applications to the $\\displaystyle L^{r}$ Hodge theory in a compact riemannian manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Eric Amar (IMB)","submitted_at":"2015-06-01T10:09:46Z","abstract_excerpt":"Let $X$ be a complete metric space and $\\displaystyle \\Omega $ a domain in $\\displaystyle X.$ The Raising Steps Method allows to get from local results on solutions $u$ of a linear equation $\\displaystyle Du=\\omega $ global ones in $\\displaystyle \\Omega .$\\ \nIt was introduced in \\cite{AmarSt13} to get good estimates on solutions of $\\bar \\partial $ equation in domains in a Stein manifold. As a simple application we shall get a strong $\\displaystyle L^{r}$ Hodge decomposition theorem for $p-$forms in a compact riemannian manifold without boundary, and then we retrieve this known result by an en"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00418","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"}