{"id":"W2337216489","doi":"10.1007/s00222-016-0688-y","title":"Curvature estimates for immersed hypersurfaces in Riemannian manifolds","year":2016,"lang":"en","type":"article","venue":"Inventiones mathematicae","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":28,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University","funders":"","keywords":"Scalar curvature; Embedding; Hypersurface; Riemannian manifold; Riemann curvature tensor; Manifold (fluid mechanics); Mathematical analysis; Prescribed scalar curvature problem; Mathematics; Ricci-flat manifold; Sectional curvature; Curvature; Ricci curvature; Pure mathematics; Mathematical physics; Physics; Geometry","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003313951,0.002562801,0.001414437,0.008610816,0.00152377,0.003591401,0.002151147,0.001894309,0.006715422],"category_scores_gemma":[0.01090176,0.0008725504,0.001579829,0.0020998,0.004031325,0.008254975,0.005833754,0.005871431,0.0009568075],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003169108,"about_ca_system_score_gemma":0.0008420592,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002912267,"about_ca_topic_score_gemma":0.00241195,"domain_scores_codex":[0.998951,0.0003672144,0.00006795616,0.0001592732,0.0003343707,0.0001201096],"domain_scores_gemma":[0.9951494,0.001941253,0.000677495,0.0003372405,0.0008818119,0.0010128],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00006087896,0.00003958591,0.001033238,0.0001463122,0.00005281966,0.000145332,0.0007031642,0.004957403,0.003549137,0.9783137,0.002297862,0.008700666],"study_design_scores_gemma":[0.00001530238,0.00005884992,0.001836169,0.00007696867,0.00004882731,0.0001655104,0.0003042971,0.04901706,0.001156246,0.9407817,0.006486309,0.00005279461],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3662784,0.01517176,0.5426819,0.008294127,0.001103378,0.0001348057,0.0006991359,0.000731973,0.0649045],"genre_scores_gemma":[0.8737249,0.008864046,0.07024651,0.0009310697,0.002034196,0.0001615627,0.001040258,0.0006788116,0.04231864],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008610816,"threshold_uncertainty_score":0.02299356,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06167924045479872,"score_gpt":0.3257783473697869,"score_spread":0.2640991069149882,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}