{"paper":{"title":"A Moser/Bernstein type theorem in a Lie group with a left invariant metric under a gradient decay condition","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ari Aiolfi, Jaime Ripoll, Leonardo Bonorino, Marc Soret, Marina Ville","submitted_at":"2021-08-05T20:52:48Z","abstract_excerpt":"We say that a PDE in a Riemannian manifold $M$ is geometric if,$\\ $whenever $u$ is a solution of the PDE on a domain $\\Omega$ of $M$, the composition $u_{\\phi}:=u\\circ\\phi$ is also solution on $\\phi^{-1}\\left( \\Omega\\right) $, for any isometry $\\phi$ of $M.$ We prove that if $u\\in C^{1}\\left( \\mathbb{H}^{n}\\right) $ is a solution of a geometric PDE satisfying the comparison principle, where $\\mathbb{H}^{n}$ is the hyperbolic space of constant sectional curvature $-1,$ $n\\geq2,$ and if \\[ \\limsup_{R\\rightarrow\\infty}\\left( e^{R}\\sup_{S_{R}}\\left\\Vert \\nabla u\\right\\Vert \\right) =0, \\] where $S_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.02844","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/2108.02844/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"}