{"paper":{"title":"The Diederich-Forn{\\ae}ss index I: for domains of non-trivial index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Bingyuan Liu","submitted_at":"2017-01-01T22:22:46Z","abstract_excerpt":"We study bounded pseudoconvex domains in complex Euclidean space. We define an index associated to the boundary and show this new index is equivalent to the Diederich-Forn{\\ae}ss index defined in 1977. This connects the Diederich-Forn{\\ae}ss index to boundary conditions and refines the Levi pseudoconvexity. We also prove the $\\beta$-worm domain is of index $\\pi/{(2\\beta)}$. It is the first time that a precise non-trivial Diederich-Forn{\\ae}ss index in Euclidean spaces is obtained. This finding also indicates that the Diederich-Forn{\\ae}ss index is a continuum in $(0,1]$, not a discrete set. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00293","kind":"arxiv","version":4},"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"}