{"paper":{"title":"On Competing Definitions for the Diederich-Forn{\\ae}ss Index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Phillip S. Harrington","submitted_at":"2019-07-08T15:52:20Z","abstract_excerpt":"Let $\\Omega\\subset\\mathbb{C}^n$ be a bounded pseudoconvex domain. We define the Diederich-Forn{\\ae}ss index with respect to a family of functions to be the supremum over the set of all exponents $0<\\eta<1$ such that there exists a function $\\rho_\\eta$ in this family such that $-\\rho_\\eta$ is comparable to the distance to the boundary of $\\Omega$ on $\\Omega$ and such that $-(-\\rho_\\eta)^\\eta$ is plurisubharmonic on $\\Omega$. We first prove that computing the Diederich-Forn{\\ae}ss index with respect to the family of upper semi-continuous functions is the same as computing the Diederich-Forn{\\ae}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03689","kind":"arxiv","version":1},"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"}