{"paper":{"title":"Restriction estimates in a conical singular space: wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiqiang Zheng, Junyong Zhang, Xiaofen Gao","submitted_at":"2020-07-10T04:41:52Z","abstract_excerpt":"We study the restriction estimates in a class of conical singular space $X=C(Y)=(0,\\infty)_r\\times Y$ with the metric $g=\\mathrm{d}r^2+r^2h$, where the cross section $Y$ is a compact $(n-1)$-dimensional closed Riemannian manifold $(Y,h)$. Let $\\Delta_g$ be the Friedrich extension positive Laplacian on $X$, and consider the operator $\\mathcal{L}_V=\\Delta_g+V$ with $V=V_0r^{-2}$, where $V_0(\\theta)\\in\\mathcal{C}^\\infty(Y)$ is a real function such that the operator $\\Delta_h+V_0+(n-2)^2/4$ is positive. In the present paper, we prove a type of modified restriction estimates for the solutions of wa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.05161","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/2007.05161/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"}