{"paper":{"title":"Phragm\\'en-Lindel\\\"of theorems and p-harmonic measures for sets near low-dimensional hyperplanes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Niklas L.P. Lundstr\\\"Om","submitted_at":"2015-03-18T13:05:24Z","abstract_excerpt":"We prove estimates of a $p$-harmonic measure, $p \\in (n-m, \\infty]$, for sets in $\\mathbf{R}^n$ which are close to an $m$-dimensional hyperplane $\\Lambda \\subset \\mathbf{R}^n$, $m \\in [0,n-1]$. Using these estimates, we derive results of Phragm\\'en-Lindel\\\"of type in unbounded domains $\\Omega \\subset \\mathbf{R}^n\\setminus \\Lambda$ for $p$-subharmonic functions. Moreover, we give local and global growth estimates for $p$-harmonic functions, vanishing on sets in $\\mathbf{R}^n$, which are close to an $m$-dimensional hyperplane."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05382","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"}