{"id":"W1969646564","doi":"10.1007/s00208-010-0555-x","title":"Sharp convex Lorentz–Sobolev inequalities","year":2010,"lang":"de","type":"article","venue":"Mathematische Annalen","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":97,"is_retracted":false,"has_abstract":false,"ca_institutions":"Memorial University of Newfoundland","funders":"","keywords":"Isoperimetric inequality; Mathematics; Lorentz transformation; Lipschitz continuity; Regular polygon; Pure mathematics; Minkowski space; Sobolev inequality; Inequality; Mathematical analysis; Sobolev space; Mathematical physics; Geometry; Physics; Classical mechanics","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":[0.002743203,0.00175993,0.001003352,0.00297001,0.001099362,0.002848173,0.001368193,0.001630762,0.006771233],"category_scores_gemma":[0.007809627,0.0006279277,0.001050582,0.00167435,0.00413901,0.005978981,0.003089955,0.007026346,0.001001914],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002060486,"about_ca_system_score_gemma":0.0006734225,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00162475,"about_ca_topic_score_gemma":0.001149416,"domain_scores_codex":[0.9989242,0.0004261108,0.0000416113,0.0001633834,0.0003082677,0.000136479],"domain_scores_gemma":[0.9967862,0.001812757,0.000349916,0.0002350948,0.0004800661,0.0003359446],"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":[0.00002193496,0.000008487302,0.0001268492,0.00003939488,0.00001079141,0.00003741082,0.0001027416,0.001818389,0.0006533084,0.992316,0.001240874,0.003623807],"study_design_scores_gemma":[0.000008467451,0.00001232322,0.0003533958,0.00001581921,0.00001033172,0.00004957919,0.00004831517,0.01315879,0.0004263129,0.9814613,0.004441645,0.00001369063],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1625175,0.010527,0.6184431,0.01195154,0.0009924801,0.00008140668,0.0008502234,0.0003506957,0.194286],"genre_scores_gemma":[0.8687198,0.008162423,0.06925993,0.002503159,0.001777161,0.0002053901,0.0006059981,0.0002391698,0.04852691],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006771233,"threshold_uncertainty_score":0.02265203,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06060825728206195,"score_gpt":0.3187404402590165,"score_spread":0.2581321829769546,"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."}}