{"paper":{"title":"Constant mean curvature, flux conservation, and symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bruce Solomon, Nick Edelen","submitted_at":"2013-02-13T16:05:09Z","abstract_excerpt":"As first noted in Korevaar, Kusner and Solomon (\"KKS\"), constant mean curvature implies a homological conservation law for hypersurfaces in ambient spaces with Killing fields.In Theorem 3.5 here, we generalize that law by relaxing the topological restrictions assumed in [KKS] and by allowing a weighted mean curvature functional. We also prove a partial converse (Theorem 4.1) which roughly says that when flux is conserved along a Killing field, a hypersurface splits into two regions: one with constant (weighted) mean curvature, and one preserved by the Killing field. We demonstrate our theory b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3149","kind":"arxiv","version":4},"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"}