{"paper":{"title":"Convex hypersurfaces of prescribed curvatures in hyperbolic space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Li Chen","submitted_at":"2023-02-03T09:01:16Z","abstract_excerpt":"For a smooth, closed and uniformly $h$-convex hypersurface $M$ in $\\mathbb{H}^{n+1}$, the horospherical Gauss map $G: M \\rightarrow \\mathbb{S}^n$ is a diffeomorphism. We consider the problem of finding a smooth, closed and uniformly $h$-convex hypersurface $M\\subset \\mathbb{H}^{n+1}$ whose $k$-th shifted mean curvature $\\widetilde{H}_{k}$ ($1\\leq k\\leq n$) is prescribed as a positive function $\\tilde{f}(x)$ defined on $\\mathbb{S}^n$, i.e. \\begin{eqnarray*} \\widetilde{H}_{k}(G^{-1}(x))=\\tilde{f}(x). \\end{eqnarray*} We can prove the existence of solution to this problem if the given function $\\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.01604","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/2302.01604/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"}