{"paper":{"title":"Geometric Analysis on the Diederich-Forn{\\ae}ss Index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Bingyuan Liu, Marco Peloso, Steven G. Krantz","submitted_at":"2016-06-07T21:59:23Z","abstract_excerpt":"We derive a sufficient condition on a bounded pseudoconvex domain $\\Omega\\subset\\mathbb{C}^2$ with smooth boundary such that $-(-\\rho)^\\eta$ is plurisubharmonic on $\\Omega$ for $\\eta>0$ arbitrarily close to $1$ (the supremum of $\\eta$ is called Diederich-Forn{\\ae}ss index, see Definition  (df)). This condition (see Theorem prop) extends a theorem of Forn{\\ae}ss and Herbig in 2007 and only requires restriction on Levi-flat sets of the boundary $\\partial\\Omega$. Since the condition is on Levi-flat sets, it contains more geometric information. As an application of this new condition, we discuss h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02343","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"}