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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1706.08084","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-06-25T11:58:27Z","cross_cats_sorted":[],"title_canon_sha256":"ffa13203aa21a8478852074ea2ddfa399bdbb7f350b24f55424f6342c0965b82","abstract_canon_sha256":"2f892cfbd74a5a77381e580c949cc0db8d37964a79adf8e0852128f6393bedcb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:46.308294Z","signature_b64":"gntiyiHWH/+yUYng1/ygtK+gP06TgGqn0o5Gfb7z9GNg+FKxrRr8/0Ff9Nf4SyWKcYkFW7iRP7ZTTwuI/cNsAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74ce6555f56525f24448d262de460835e191680fab5eebda92563f3a1d11375a","last_reissued_at":"2026-05-18T00:05:46.307807Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:46.307807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1706.08084","created_at":"2026-05-18T00:05:46.307878+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.08084v2","created_at":"2026-05-18T00:05:46.307878+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08084","created_at":"2026-05-18T00:05:46.307878+00:00"},{"alias_kind":"pith_short_12","alias_value":"OTHGKVPVMUS7","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"OTHGKVPVMUS7ERCI","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"OTHGKVPV","created_at":"2026-05-18T12:31:34.259226+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OTHGKVPVMUS7ERCI2JRN4RQIGX","json":"https://pith.science/pith/OTHGKVPVMUS7ERCI2JRN4RQIGX.json","graph_json":"https://pith.science/api/pith-number/OTHGKVPVMUS7ERCI2JRN4RQIGX/graph.json","events_json":"https://pith.science/api/pith-number/OTHGKVPVMUS7ERCI2JRN4RQIGX/events.json","paper":"https://pith.science/paper/OTHGKVPV"},"agent_actions":{"view_html":"https://pith.science/pith/OTHGKVPVMUS7ERCI2JRN4RQIGX","download_json":"https://pith.science/pith/OTHGKVPVMUS7ERCI2JRN4RQIGX.json","view_paper":"https://pith.science/paper/OTHGKVPV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.08084&json=true","fetch_graph":"https://pith.science/api/pith-number/OTHGKVPVMUS7ERCI2JRN4RQIGX/graph.json","fetch_events":"https://pith.science/api/pith-number/OTHGKVPVMUS7ERCI2JRN4RQIGX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OTHGKVPVMUS7ERCI2JRN4RQIGX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OTHGKVPVMUS7ERCI2JRN4RQIGX/action/storage_attestation","attest_author":"https://pith.science/pith/OTHGKVPVMUS7ERCI2JRN4RQIGX/action/author_attestation","sign_citation":"https://pith.science/pith/OTHGKVPVMUS7ERCI2JRN4RQIGX/action/citation_signature","submit_replication":"https://pith.science/pith/OTHGKVPVMUS7ERCI2JRN4RQIGX/action/replication_record"}},"created_at":"2026-05-18T00:05:46.307878+00:00","updated_at":"2026-05-18T00:05:46.307878+00:00"}