{"paper":{"title":"Gromov hyperbolicity and the Kobayashi metric on \"convex\" sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Maria Trybula, Nikolai Nikolov","submitted_at":"2017-06-25T11:58:27Z","abstract_excerpt":"In this paper we study the global geometry of the Kobayashi metric on \"convex\" sets. We provide new examples of non-Gromov hyperbolic domains in $\\mathbb{C}^n$ of many kinds: pseudoconvex and non-pseudocon \\newline -vex, bounded and unbounded. Our first aim is to prove that if $\\Omega$ is a bounded weakly linearly convex domain in $\\mathbb{C}^n,\\,n\\geq 2,$ and $S$ is an affine complex hyperplane intersecting $\\Omega,$ then the domain $\\Omega\\setminus S$ endowed with the Kobayashi metric is not Gromov hyperbolic (Theorem 1.3). Next we localize this result on Kobayashi hyperbolic convex domains."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08084","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"}