{"paper":{"title":"Induced Fubini-Study metrics on strictly pseudoconvex CR manifolds and zeros of random CR functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","math.DG","math.PR"],"primary_cat":"math.CV","authors_text":"Chin-Yu Hsiao, George Marinescu, Hendrik Herrmann, Wei-Chuan Shen","submitted_at":"2024-01-17T11:34:33Z","abstract_excerpt":"Let $X$ be a compact strictly pseudoconvex embeddable Cauchy-Riemann manifold and let $T_P$ be the Toeplitz operator on $X$ associated with a first-order pseudodifferential operator $P$. In our previous work we established the asymptotic expansion for $k$ large of the kernel of the operators $\\chi(k^{-1}T_P)$, where $\\chi$ is a smooth cut-off function supported in the positive real line. By using these asymptotics, we show in this paper that $X$ can be projectively embedded by maps with components of the form $\\chi(k^{-1}\\lambda)f_\\lambda$, where $\\lambda$ is an eigenvalue of $T_P$ and $f_\\lam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.09143","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/2401.09143/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"}