{"paper":{"title":"Travelling graphs for the forced mean curvature motion in an arbitrary space dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jean-Michel Roquejoffre (IMT), R\\'egis Monneau (CERMICS), Violaine Roussier-Michon (IMT)","submitted_at":"2011-07-05T15:10:20Z","abstract_excerpt":"We construct travelling wave graphs of the form $z=-ct+\\phi(x)$, $\\phi: x \\in \\mathbb{R}^{N-1} \\mapsto \\phi(x)\\in \\mathbb{R}$, $N \\geq 2$, solutions to the $N$-dimensional forced mean curvature motion $V_n=-c_0+\\kappa$ ($c\\geq c_0$) with prescribed asymptotics. For any 1-homogeneous function $\\phi_{\\infty}$, viscosity solution to the eikonal equation $|D\\phi_{\\infty}|=\\sqrt{(c/c_0)^2-1}$, we exhibit a smooth concave solution to the forced mean curvature motion whose asymptotics is driven by $\\phi_{\\infty}$. We also describe $\\phi_{\\infty}$ in terms of a probability measure on $\\mathbb{S}^{N-2}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0896","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"}