{"paper":{"title":"Lagrange multipliers and adiabatic limits I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP","math.SG"],"primary_cat":"math.DG","authors_text":"Joa Weber, Urs Frauenfelder","submitted_at":"2022-10-18T21:22:52Z","abstract_excerpt":"Critical points of a function subject to a constraint can be either detected by restricting the function to the constraint or by looking for critical points of the Lagrange multiplier functional. Although the critical points of the two functionals, namely the restriction and the Lagrange multiplier functional are in natural one-to-one correspondence this does not need to be true for their gradient flow lines. We consider a singular deformation of the metric and show by an adiabatic limit argument that close to the singularity we have a one-to-one correspondence between gradient flow lines conn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.11221","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2210.11221/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"}