{"paper":{"title":"Riemannian Penrose Inequality for Manifolds with Corners via Non-Linear Potential Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Christina Karapiperi, Lorenzo Mazzieri, Virginia Agostiniani","submitted_at":"2026-06-25T15:25:04Z","abstract_excerpt":"We present a new proof of the Positive Mass Theorem and the Riemannian Penrose Inequality for three-dimensional asymptotically flat Riemannian manifolds whose metrics fail to be $C^1$ across a hypersurface $\\Sigma$, first proven by Miao and McCormick-Miao, respectively. Unlike these approaches, ours recovers these results directly, without relying on their original formulations for smooth metrics. The proofs are based on a unified argument which applies to both theorems. We achieve this by establishing an approximate monotonicity for the quantity introduced by Agostiniani-Mantegazza-Mazzieri-O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27155","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/2606.27155/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"}