{"paper":{"title":"Totally geodesic discs in strongly convex domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Harish Seshadri, Herve Gaussier","submitted_at":"2012-01-24T10:42:38Z","abstract_excerpt":"We prove that Kobayashi isometries between strongly convex domains are holomorphic or anti-holomorphic.\n  More precisely, let $n_1, n_2$ be positive integers and let $\\Omega_i \\subset \\C^{n_i}, \\ i=1,2$, be bounded $C^3$ strongly convex domains. If $\\phi: (\\Omega_1, d^K_{\\Omega_1}) \\rightarrow (\\Omega_2, d^K_{\\Omega_2})$ is an isometry, i.e. $ d^K_\\Omega_{n_2}(f(\\zeta),f(\\eta)) = d^K_{n_1} (\\zeta,\\eta)$ for all $\\zeta,\\eta \\in \\Omega_1,$ then $\\phi$ is either holomorphic or anti-holomorphic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4944","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"}