{"paper":{"title":"Quantitative Lorentzian isoperimetric inequalities in conical Minkowski spacetimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Lorentzian isoperimetric inequalities admit optimal stability estimates measured by Fraenkel asymmetry with universal constants.","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.DG","authors_text":"Christian Lange, Jonas W. Peteranderl","submitted_at":"2025-10-30T17:47:53Z","abstract_excerpt":"We establish optimal stability estimates in terms of the Fraenkel asymmetry with universal dimensional constants for a Lorentzian isoperimetric inequality due to Bahn and Ehrlich and, as a consequence, for a special version of a Lorentzian isoperimetric inequality due to Cavalletti and Mondino. For the Bahn--Ehrlich inequality the Fraenkel asymmetry enters the stability result quadratically like in the Euclidean case while for the Cavalletti--Mondino inequality the Fraenkel asymmetry enters linearly. As it turns out, refining the latter inequality through an additional geometric term allows us"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish optimal stability estimates in terms of the Fraenkel asymmetry with universal dimensional constants for a Lorentzian isoperimetric inequality due to Bahn and Ehrlich and, as a consequence, for a special version of a Lorentzian isoperimetric inequality due to Cavalletti and Mondino.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The upgrade to Hausdorff stability relies on working inside a fixed conical Minkowski spacetime that supplies a natural Lipschitz bound from the causal structure; this assumption is invoked in the final section when the distance of Bahn and Ehrlich is applied to Cauchy hypersurfaces.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Optimal stability estimates are established for Lorentzian isoperimetric inequalities of Bahn-Ehrlich and Cavalletti-Mondino using Fraenkel asymmetry, with quadratic or linear dependence and an upgrade to Hausdorff stability in conical Minkowski spacetime.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Lorentzian isoperimetric inequalities admit optimal stability estimates measured by Fraenkel asymmetry with universal constants.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ca540cb3f2d10c22042de06d936b319dd7753353daa6d90e634b2fae8a5d03be"},"source":{"id":"2510.26755","kind":"arxiv","version":3},"verdict":{"id":"cb678f8e-c0f3-4221-9a2d-6126d72919b8","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-18T02:48:49.547351Z","strongest_claim":"We establish optimal stability estimates in terms of the Fraenkel asymmetry with universal dimensional constants for a Lorentzian isoperimetric inequality due to Bahn and Ehrlich and, as a consequence, for a special version of a Lorentzian isoperimetric inequality due to Cavalletti and Mondino.","one_line_summary":"Optimal stability estimates are established for Lorentzian isoperimetric inequalities of Bahn-Ehrlich and Cavalletti-Mondino using Fraenkel asymmetry, with quadratic or linear dependence and an upgrade to Hausdorff stability in conical Minkowski spacetime.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The upgrade to Hausdorff stability relies on working inside a fixed conical Minkowski spacetime that supplies a natural Lipschitz bound from the causal structure; this assumption is invoked in the final section when the distance of Bahn and Ehrlich is applied to Cauchy hypersurfaces.","pith_extraction_headline":"Lorentzian isoperimetric inequalities admit optimal stability estimates measured by Fraenkel asymmetry with universal constants."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.26755/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":2,"snapshot_sha256":"0bd30855a9d0dfa829dc1ddbfbc45d8ae4311c6e635e3ba57b646d63906c9317"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}