{"paper":{"title":"Translating solitons of the mean curvature flow asymptotic to hyperplanes in $\\mathbb{R}^{n+1}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Eddygledson S. Gama, Francisco Martin","submitted_at":"2018-02-23T10:15:46Z","abstract_excerpt":"A translating soliton is a hypersurface $M$ in $\\mathbb{R}^{n+1}$ such that the family $M_t= M- t \\,\\mathbf{e}_{n+1}$ is a mean curvature flow, i.e., such that normal component of the velocity at each point is equal to the mean curvature at that point $\\mathbf{H}=\\mathbf{e}_{n+1}^{\\perp}.$ In this paper we obtain a characterization of hyperplanes which are parallel to $\\mathbf{e}_{n+1}$ and the family of tilted grim reaper cylinders as the only translating solitons in $\\mathbb{R}^{n+1}$ which are $C^1$-asymptotic to two half-hyperplanes outside a non-vertical cylinder. This result was proven f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08468","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"}