{"paper":{"title":"Minimal 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":"2014-10-09T16:10:22Z","abstract_excerpt":"We study surfaces in Euclidean space ${\\mathbb R}^3$ that are minimal for a log-linear density $\\phi(x,y,z)=\\alpha x+\\beta y+\\gamma y$, where $\\alpha,\\beta,\\gamma$ are real numbers not all zero. We prove that if a surface is $\\phi$-minimal foliated by circles in parallel planes, then these planes are orthogonal to the vector $(\\alpha,\\beta,\\gamma)$ and the surface must be rotational. We also classify all minimal surfaces of translation type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2517","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"}