{"id":"W2963682522","doi":"10.4171/jst/143","title":"Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound","year":2016,"lang":"en","type":"article","venue":"Journal of Spectral Theory","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":24,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"Fonds de recherche du Québec – Nature et technologies; Natural Sciences and Engineering Research Council of Canada; Canada Research Chairs","keywords":"Ricci curvature; Curvature of Riemannian manifolds; Mathematics; Pure mathematics; Curvature; Sectional curvature; Ricci flow; Ricci-flat manifold; Eigenvalues and eigenvectors; Mathematical analysis; Scalar curvature; Upper and lower bounds; Physics; Geometry","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001691554,0.0002683458,0.0005668715,0.0003954777,0.00009947905,0.0000838183,0.0003519599,0.000140466,0.001229531],"category_scores_gemma":[0.0004557252,0.0001257708,0.0003557141,0.0004913984,0.0001060605,0.0003020667,0.00002520737,0.0004115985,0.00004652106],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000120801,"about_ca_system_score_gemma":0.00008906102,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001881129,"about_ca_topic_score_gemma":0.00001066511,"domain_scores_codex":[0.9979271,0.0001959739,0.0005984305,0.000185007,0.0007339684,0.0003595133],"domain_scores_gemma":[0.9979407,0.0006176745,0.0006649141,0.0003592203,0.0002497562,0.0001677807],"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":[0.001378533,0.0005208736,0.00119453,0.00005307417,0.0009287713,0.0004062894,0.0008768299,0.000008544856,0.0005742346,0.9808217,0.01056996,0.002666613],"study_design_scores_gemma":[0.001843915,0.002133068,0.003114212,0.0005929058,0.0004934954,0.0002822393,0.001084219,0.000003274151,0.001665424,0.9736626,0.01468147,0.0004432448],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9729372,0.00088569,0.007876088,0.001302305,0.0003856185,0.0001199976,0.000009634444,0.0000318103,0.0164516],"genre_scores_gemma":[0.9884188,0.0001276532,0.001817104,0.0002461353,0.0008768766,0.000001898472,4.203615e-7,0.00004020776,0.008470865],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01548159,"threshold_uncertainty_score":0.9996835,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02547267627306345,"score_gpt":0.273006342265581,"score_spread":0.2475336659925175,"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."}}