{"paper":{"title":"Hartogs Domains and the Diederich Forn{\\ae}ss Index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Muhenned Abdulsahib, Phillip S. Harrington","submitted_at":"2018-09-07T20:24:53Z","abstract_excerpt":"We study a geometric property of the boundary on Hartogs domains which can be used to find upper and lower bounds for the Diederich-Forn{\\ae}ss Index. Using this, we are able to show that under some reasonable hypotheses on the set of weakly pseudoconvex points, the Diederich-Forn{\\ae}ss Index for a Hartogs domain is equal to one if and only if the domain admits a family of good vector fields in the sense of Boas and Straube. We also study the analogous problem for a Stein neighborhood basis, and show that under the same hypotheses if the Diederich-Forn{\\ae}ss Index for a Hartogs domain is equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02662","kind":"arxiv","version":3},"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"}