{"paper":{"title":"Invariant surfaces in Euclidean space with a log-linear density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Rafael L\\'opez","submitted_at":"2018-02-22T11:38:57Z","abstract_excerpt":"A $\\lambda$-translating soliton with density vector $\\vec{v}$ is a surface in Euclidean space whose mean curvature $H$ satisfies $2H=2\\lambda+\\langle N,\\vec{v}\\rangle$, where $N$ is the Gauss map. We classify all $\\lambda$-translating solitons that are invariant by a one-parameter group of translations and a one-parameter group of rotations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07987","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"}