{"id":"W3132798415","doi":"10.4310/pamq.2022.v18.n2.a4","title":"A fully-nonlinear flow and quermassintegral inequalities in the sphere","year":2022,"lang":"en","type":"article","venue":"Pure and Applied Mathematics Quarterly","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":29,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"","keywords":"Curvature; Regular polygon; Flow (mathematics); Mathematics; Nonlinear system; Focus (optics); Convergence (economics); Forcing (mathematics); Space (punctuation); Set (abstract data type); Current (fluid); Term (time); Mean curvature flow; Inequality; Mathematical analysis; Applied mathematics; Mathematical optimization; Computer science; Geometry; Physics; Mean curvature; Optics; Economics","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":[0.000650094,0.0005075335,0.0003257118,0.0005716807,0.00047761,0.0009619197,0.0003460637,0.0004051143,0.004056372],"category_scores_gemma":[0.001607134,0.0001227153,0.0005288044,0.0002874112,0.001884022,0.001983389,0.001540401,0.001238397,0.0003320542],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007831051,"about_ca_system_score_gemma":0.0003686831,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001527496,"about_ca_topic_score_gemma":0.001198908,"domain_scores_codex":[0.9997064,0.00009874037,0.00001665056,0.00007319527,0.00007005909,0.0000348094],"domain_scores_gemma":[0.9994084,0.0002734246,0.00008465995,0.00005137511,0.0001023797,0.00007983828],"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":[0.00001974534,0.000004820225,0.0003643136,0.00007777372,0.00001013706,0.00009402852,0.00008767131,0.006091886,0.002299741,0.9838068,0.0008955197,0.006247447],"study_design_scores_gemma":[0.000008365688,0.00007169956,0.002004165,0.00005133445,0.00001531541,0.0002944679,0.0001346301,0.07183109,0.001666747,0.9091672,0.01472945,0.00002544748],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2660909,0.007671605,0.615491,0.005104823,0.0004790507,0.00004825527,0.0006326709,0.0001586147,0.1043231],"genre_scores_gemma":[0.9357415,0.003628393,0.04046722,0.0006485416,0.00051706,0.00004785515,0.0002941787,0.00007134811,0.01858398],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004056372,"threshold_uncertainty_score":0.01356989,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02474439643522938,"score_gpt":0.2526235268985798,"score_spread":0.2278791304633504,"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."}}