{"paper":{"title":"Sharp thresholds for the Escobar functional: the Escobar-Willmore mass, geometric selection, and compactness trichotomy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.DG","authors_text":"Mayukh Mukherjee, Utsab Sarkar","submitted_at":"2026-01-30T07:34:16Z","abstract_excerpt":"We study the hemisphere threshold for the conformally covariant Escobar functional on compact Riemannian manifolds $(M^n,g)$ with boundary. The near-threshold landscape is organized by boundary invariants: the first-order coefficient $\\rho_n^{\\mathrm{conf}}H_g$ vanishes identically, so the leading obstruction is a renormalized boundary mass $\\mathfrak R_g$ (second order, $n\\ge5$), followed by a cubic invariant $\\Theta_g$ (third order, $n\\ge6$), with a Green kernel interaction $\\mathsf G_\\partial$ in the multi-bubble regime.\n  Exact evaluation of weighted profile moments yields $\\kappa_1=\\kappa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.22665","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/2601.22665/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"}