{"id":"W4388204721","doi":"10.1007/s00526-023-02598-0","title":"Curvature estimates for semi-convex solutions of Hessian equations in hyperbolic space","year":2023,"lang":"en","type":"article","venue":"Calculus of Variations and Partial Differential Equations","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Hessian equation; Hessian matrix; Curvature; Regular polygon; Space (punctuation); Hyperbolic space; Mathematical analysis; Pure mathematics; Applied mathematics; Geometry; Partial differential equation","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002937795,0.001971445,0.001257263,0.005135025,0.001143265,0.002779398,0.001764453,0.001326905,0.004342794],"category_scores_gemma":[0.0101733,0.0007638616,0.001138177,0.001368404,0.002880682,0.005554271,0.003565298,0.003764067,0.0005552237],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002863482,"about_ca_system_score_gemma":0.001134392,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003330524,"about_ca_topic_score_gemma":0.003396611,"domain_scores_codex":[0.9992771,0.0002471409,0.00004463803,0.0001041892,0.0002305774,0.00009635142],"domain_scores_gemma":[0.9947394,0.002163997,0.0006569415,0.0002614485,0.001095305,0.001082961],"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":[0.00007095389,0.00006295887,0.001037794,0.0001319662,0.00004791056,0.0001369835,0.0005037002,0.01378439,0.005327359,0.9679714,0.00227083,0.008653741],"study_design_scores_gemma":[0.00001697577,0.00008042464,0.002705947,0.00007511099,0.0000393798,0.0001659869,0.0003224914,0.2117798,0.001730468,0.7796393,0.003370806,0.00007339443],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3502261,0.005780578,0.5911085,0.004434884,0.0005239865,0.0001424772,0.0005205701,0.0004351543,0.04682776],"genre_scores_gemma":[0.9112707,0.003205636,0.04829517,0.0005388162,0.0006116887,0.0001204928,0.0005183375,0.0003272893,0.03511177],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005135025,"threshold_uncertainty_score":0.02077609,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06991411757903936,"score_gpt":0.3236177314684085,"score_spread":0.2537036138893691,"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."}}