{"paper":{"title":"Multiple Delaunay ends solutions of the Cahn-Hilliard equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Matteo Rizzi, Michal Kowalczyk","submitted_at":"2018-10-02T20:15:03Z","abstract_excerpt":"Let $\\Sigma$ be a surface of constant mean curvature in ${\\mathbb R}^3$ with multiple Delaunay ends. Assuming that $\\Sigma$ is non degenerate in this paper we construct new solutions to the Cahn-Hilliard equation $\\varepsilon\\Delta u+\\varepsilon^{-1}u(1-u^2)=\\ell_\\varepsilon$ in ${\\mathbb R}^3$ such that as $\\varepsilon\\to 0$ the zero level set of $u_\\varepsilon$ approaches $\\Sigma$. Moreover, on compacts of the connected components of ${\\mathbb R}^3\\setminus \\Sigma$ we have $1-|u_\\varepsilon|\\to 0$ uniformly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01494","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":""},"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"}