{"paper":{"title":"Translating solutions to the Gauss curvature flow with flat sides","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ki-Ahm Lee, Kyeongsu Choi, Panagiota Daskalopoulos","submitted_at":"2016-10-23T17:47:54Z","abstract_excerpt":"We derive local $C^{2}$ estimates for complete non-compact translating solitons of the Gauss curvature flow in $\\mathbb{R}^3$ which are graphs over a convex domain $\\Omega$. This is closely is related to deriving local $C^{1,1}$ estimates for the degenerate Monge-Amp\\'ere equation. As a result, given a weakly convex bounded domain $\\Omega$, we establish the existence of a $C^{1,1}_{\\text{loc}}$ translating soliton. In particular, when the boundary $\\partial \\Omega$ has a line segment, we show the existence of flat sides of the translator from a local a'priori non-degeneracy estimate near the f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07206","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"}