{"paper":{"title":"Sharp One-bubble Critical-Point Stability and Global Compactness for the Sobolev Trace Inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bao Yu, Yang Zhou","submitted_at":"2026-07-23T15:31:39Z","abstract_excerpt":"Let $n\\ge3$ and $1<p<n$. We first prove the local trace analogue of the sharp one-bubble critical-point stability theorem of Liu and Zhang~\\cite{LiuZhang2025}: near a positive trace-bubble, the Euler--Lagrange residual controls the gradient distance to the normalized trace-bubble manifold with the sharp power $\\max\\{1,p-1\\}$. Then, we establish a Struwe-type compactness theorem for the critical trace functional, which gives the trace counterpart of the Mercuri--Willem decomposition~\\cite{MercuriWillem2010}. Combining Struwe-type compactness with the local stability estimate yields a sharp quan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21429","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/2607.21429/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"}