{"paper":{"title":"Invariant $\\lambda$-translators for the Gauss curvature flow in Euclidean space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Muhittin Evren Aydin, Rafael L\\'opez","submitted_at":"2025-08-24T12:01:58Z","abstract_excerpt":"A $\\lambda$-translator is a surface in Euclidean space $\\mathbb{R}^3$ whose Gauss curvature $K$ satisfies $K=\\langle N, \\vec{v} \\rangle +\\lambda$, where $N$ is the Gauss map, $\\vec{v}$ is a fixed direction, and $\\lambda \\in \\mathbb{R}$. In this paper, we classify all $\\lambda$-translators 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":"2508.17321","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.17321/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}