{"paper":{"title":"Bounded Plurisubharmonic Exhaustion Functions for Lipschitz Pseudoconvex Domains in $\\mathbb{CP}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Phillip S. Harrington","submitted_at":"2015-10-13T15:18:32Z","abstract_excerpt":"In this paper, we use Takeuchi's Theorem to show that for every Lipschitz pseudoconvex domain $\\Omega$ in $\\mathbb{CP}^n$ there exists a Lipschitz defining function $\\rho$ and an exponent $0<\\eta<1$ such that $-(-\\rho)^\\eta$ is strictly plurisubharmonic on $\\Omega$. This generalizes a result of Ohsawa and Sibony for $C^2$ domains. In contrast to the Ohsawa-Sibony result, we provide a counterexample demonstrating that we may not assume $\\rho=-\\delta$, where $\\delta$ is the geodesic distance function for the boundary of $\\Omega$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03737","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"}