{"paper":{"title":"On the nature of isolated asymptotic singularities of solutions of a family of quasi-linear elliptic PDE's on a Cartan-Hadamard manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jaime Bruck Ripoll, Leonardo Prange Bonorino","submitted_at":"2016-01-04T01:34:06Z","abstract_excerpt":"Let $M$ be a Cartan-Hadamard manifold with sectional curvature satisfying $-b^2\\leq K\\leq -a^2<0$, $b\\geq a>0.$ Denote by $\\partial_{\\infty}M$ the asymptotic boundary of $M$ and by $\\bar M:= M\\cup\\partial_\\infty M$ the geometric compactification of $M$ with the cone topology. We investigate here the following question: Given a finite number of points $p_{1},...,p_{k}\\in\\partial_\\infty M,$ if $u\\in C^{\\infty}(M)\\cap C^{0}\\left( \\bar{M}\\backslash\\left\\{ p_{1},...,p_{k}\\right\\} \\right) $ satisfies a PDE $\\mathcal Q(u)=0$ in $M$ and if $u|_{\\partial_\\infty M\\setminus\\left\\{p_{1},...,p_{k}\\right\\}}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00361","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1601.00361/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"}