{"paper":{"title":"Analyzing the Wu metric on a class of eggs in $\\mathbb{C}^n$ -- I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"G. P. Balakumar, Prachi Mahajan","submitted_at":"2015-03-10T07:13:08Z","abstract_excerpt":"We study the Wu metric on convex egg domains of the form \\[ E_{2m} = \\big\\{ z \\in \\mathbb{C}^n : \\vert z_1 \\vert^{2m} + \\vert z_2 \\vert^2 + \\ldots + \\vert z_{n-1} \\vert^2 + \\vert z_n \\vert^{2} <1 \\big\\} \\] where $m \\geq 1/2, m \\neq 1$. The Wu metric is shown to be real analytic everywhere except on a lower dimensional subvariety where it fails to be $C^2$-smooth. Overall however, the Wu metric is shown to be continuous when $m=1/2$ and even $C^1$-smooth for each $m>1/2$, and in all cases, a non-K\\\"ahler Hermitian metric with its holomorphic curvature strongly negative in the sense of currents."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02787","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":""},"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"}