{"paper":{"title":"Maximal subextension of $m$-subharmonic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Ayoub El-Gasmi, Hichame Amal, Sa\\\"id Asserda","submitted_at":"2026-07-21T14:24:45Z","abstract_excerpt":"In this paper, we prove that given a quasi-$m$-hyperconvex domain $\\Omega \\subset X$ in a compact K\\\"ahler manifold $(X, \\omega)$, and a function $\\varphi $ in the weighted energy class $\\mathcal{E}_\\chi^m(\\Omega, \\omega)$ with respect to a convex weight function $\\chi : \\mathbb{R} \\to \\mathbb{R}$, then there exists a maximal $\\omega$-$m$-subharmonic subextension $\\tilde{\\varphi}$ to $X$ that preserves the weighted energy and satisfies a good control properties for its Hessian measure $ \\mathbf{1}_\\Omega H_m(\\tilde{\\varphi}) \\leq \\mathbf{1}_\\Omega H_m(\\varphi) $. In the last part, we study the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19132","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/2607.19132/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"}