{"paper":{"title":"Stationary isothermic surfaces in Euclidean 3-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Peralta-Salas, Rolando Magnanini, Shigeru Sakaguchi","submitted_at":"2014-07-09T10:17:58Z","abstract_excerpt":"Let $\\Omega$ be a domain in $\\mathbb R^3$ with $\\partial\\Omega = \\partial\\left(\\mathbb R^3\\setminus \\overline{\\Omega}\\right)$, where $\\partial\\Omega$ is unbounded and connected, and let $u$ be the solution of the Cauchy problem for the heat equation $\\partial_t u= \\Delta u$ over $\\mathbb R^3,$ where the initial data is the characteristic function of the set $\\Omega^c = \\mathbb R^3\\setminus \\Omega$. We show that, if there exists a stationary isothermic surface $\\Gamma$ of $u$ with $\\Gamma \\cap \\partial\\Omega = \\varnothing$, then both $\\partial\\Omega$ and $\\Gamma$ must be either parallel planes "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2419","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"}