{"paper":{"title":"On the $L^{r}$ Hodge theory in complete non compact riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Eric Amar (IMB)","submitted_at":"2015-06-27T14:30:42Z","abstract_excerpt":"We study solutions for the Hodge laplace equation $\\Delta u=\\omega $ on $p$ forms with $\\displaystyle L^{r}$ estimates for $\\displaystyle r>1.$ Our main hypothesis is that $\\Delta $ has a spectral gap in $\\displaystyle L^{2}.$ We use this to get non classical $\\displaystyle L^{r}$ Hodge decomposition theorems. An interesting feature is that to prove these decompositions we never use the boundedness of the Riesz transforms in $\\displaystyle L^{s}.$\nThese results are based on a generalisation of the Raising Steps Method to complete non compact riemannian manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08295","kind":"arxiv","version":3},"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"}