{"paper":{"title":"On isometries of the Kobayashi and Carath\\'{e}odory metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Prachi Mahajan","submitted_at":"2010-09-13T15:06:24Z","abstract_excerpt":"This article considers isometries of the Kobayashi and Carath\\'{e}od-ory metrics on domains in $ \\mathbf{C}^n $ and the extent to which they behave like holomorphic mappings. First we prove a metric version of Poincar\\'{e}'s theorem about biholomorphic inequivalence of $ \\mathbf{B}^n $, the unit ball in $ \\mathbf{C}^n $ and $ \\Delta^n $, the unit polydisc in $ \\mathbf{C}^n $ and then provide few examples which \\textit{suggest} that $ \\mathbf{B}^n $ cannot be mapped isometrically onto a product domain. In addition, we prove several results on continuous extension of isometries $ f : D_1 \\righta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2414","kind":"arxiv","version":2},"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"}