{"paper":{"title":"The invariant Szeg\\H{o} metric on Egg 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":"2026-06-23T11:38:52Z","abstract_excerpt":"We study the Fefferman--Szeg\\H{o} metric on egg domains \\[ \\mathcal D_{2m}=\\{(z,w)\\in\\mathbb C^2: |z|^2+|w|^{2m}<1\\},\\qquad\\qquad\\qquad m\\in\\mathbb Z^+. \\] Our first main result establishes the existence of the Fefferman--Szeg\\H{o} kernel on $\\mathcal{D}_{2m}$ by verifying that the Fefferman weight lies in the Muckenhoupt class $A_2(\\partial\\mathcal{D}_{2m})$. We then derive an explicit closed-form expression for this kernel, demonstrate that its blowup occurs precisely on the boundary diagonal, and determine its boundary asymptotic behaviour. Using this kernel, we compute the associated Feffe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24452","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/2606.24452/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"}