{"paper":{"title":"On ground states for the L^2-critical boson star equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Enno Lenzmann, Rupert L. Frank","submitted_at":"2009-10-14T20:30:17Z","abstract_excerpt":"We consider ground state solutions $u \\geq 0$ for the $L^2$-critical boson star equation $$ \\sqrt{-\\Delta} \\, u - \\big (|x|^{-1} \\ast |u|^2 \\big) u = -u \\quad {in $\\R^3$}. $$ We prove analyticity and radial symmetry of $u$.\n  In a previous version of this paper, we also stated uniqueness and nondegeneracy of ground states for the $L^2$-critical boson star equation in $\\R^3$, but the arguments given there contained a gap. However, we refer to our recent preprint \\cite{FraLe} in {\\tt arXiv:1009.4042}, where we prove a general uniqueness and nondegeneracy result for ground states of nonlinear equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2721","kind":"arxiv","version":2},"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"}