{"paper":{"title":"Symmetry breaking for ground states of biharmonic NLS via Fourier extension estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enno Lenzmann, Tobias Weth","submitted_at":"2021-10-20T21:23:32Z","abstract_excerpt":"We consider ground states solutions $u \\in H^2(\\mathbb{R}^N)$ of biharmonic (fourth-order) nonlinear Schr\\\"odinger equations of the form $$ \\Delta^2 u + 2a \\Delta u + b u - |u|^{p-2} u = 0 \\quad \\mbox{in $\\mathbb{R}^N$} $$ with positive constants $a, b > 0$ and exponents $2 < p < 2^*$, where $2^* = \\frac{2N}{N-4}$ if $N > 4$ and $2^* = \\infty$ if $N \\leq 4$. By exploiting a connection to the adjoint Stein--Tomas inequality on the unit sphere and by using trial functions due to Knapp, we prove a general symmetry breaking result by showing that all ground states $u\\in H^2(\\mathbb{R}^N)$ in dimen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.10782","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.10782/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}