{"paper":{"title":"Extremizers for Fourier restriction on hyperboloids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Diogo Oliveira e Silva, Emanuel Carneiro, Mateus Sousa","submitted_at":"2017-08-12T21:44:03Z","abstract_excerpt":"The $L^2 \\to L^p$ adjoint Fourier restriction inequality on the $d$-dimensional hyperboloid $\\mathbb{H}^d \\subset \\mathbb{R}^{d+1}$ holds provided $6 \\leq p < \\infty$, if $d=1$, and $2(d+2)/d \\leq p\\leq 2(d+1)/(d-1)$, if $d\\geq2$. Quilodr\\'{a}n recently found the values of the optimal constants in the endpoint cases $(d,p)\\in\\{(2,4),(2,6),(3,4)\\}$ and showed that the inequality does not have extremizers in these cases. In this paper we answer two questions posed by Quilodr\\'{a}n, namely: (i) we find the explicit value of the optimal constant in the endpoint case $(d,p) = (1,6)$ (the remaining "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03826","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1708.03826/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"}