{"paper":{"title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jingang Xiong, Tianling Jin, Xushan Tu","submitted_at":"2025-06-10T02:53:20Z","abstract_excerpt":"This is a continuation of our earlier work [14] on the Monge-Amp\\`ere obstacle problem \\[ \\det D^2 v = v^q \\chi_{\\{v>0\\}}, \\quad v \\geq 0 \\text{ convex} \\] with $q \\in [0,n)$, where we studied the regularity of the strictly convex part of the free boundary.\n  In this work, we examine the non-strictly convex part of the free boundary and establish optimal dimension bounds for its flat portion. Additionally, we investigate the strong maximum principle and a stability property for this Monge-Amp\\`ere obstacle problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08387","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/2506.08387/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"}