{"paper":{"title":"The Invariant Szeg\\H{o} metric on strongly pseudoconvex domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Anjali Bhatnagar, Jiliang Fan","submitted_at":"2026-05-25T06:06:30Z","abstract_excerpt":"The Fefferman--Szeg\\H{o} metric \\(g_{\\operatorname{FS}}^\\Omega\\) on a \\(C^\\infty\\)-smooth bounded strongly pseudoconvex domain \\(\\Omega\\subset\\mathbb C^n\\) is an invariant metric defined via the Fefferman surface measure. For this metric, we first establish the vanishing of its \\(L^2\\)-Dolbeault cohomology outside the middle degree: \\(\\dim H^{p,q}_2(\\Omega)=0\\) if \\(p+q\\ne n\\), while \\(\\dim H^{p,q}_2(\\Omega)=\\infty\\) if \\(p+q=n\\). We also prove that the metric has \\(C^\\infty\\)-bounded geometry. Using this analytic property, we obtain several rigidity results. In particular, if the Fefferman--S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25455","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/2605.25455/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"}