Bakry–Émery curvature and model spaces in sub-Riemannian geometry
| العنوان: | Bakry–Émery curvature and model spaces in sub-Riemannian geometry |
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| المؤلفون: | Davide Barilari, Luca Rizzi |
| المساهمون: | Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Centre National de la Recherche Scientifique (CNRS), ANR-15-CE40-0018,SRGI,Géométrie sous-Riemannienne et Interactions(2015), ANR-18-CE40-0012,RAGE,Analyse Réelle et Géométrie(2018), ANR-15-CE40-0018,SRGI,Sub-Riemannian Geometry and Interactions(2015), ANR-18-CE40-0012,RAGE,REAL ANALYSIS AND GEOMETRY(2018), ANR: 11-LABX-0056,LMH,LabEx Mathématique Hadamard(2011) |
| المصدر: | Mathematische Annalen Mathematische Annalen, Springer Verlag, 2020, 377 (1-2), pp.435-482. ⟨10.1007/s00208-020-01982-x⟩ |
| بيانات النشر: | Springer Science and Business Media LLC, 2020. |
| سنة النشر: | 2020 |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, Comparison theorem, Pure mathematics, 49J15, General Mathematics, Riemannian geometry, Curvature, 01 natural sciences, symbols.namesake, Mathematics - Analysis of PDEs, 53C17, 0103 physical sciences, 0101 mathematics, Mathematics - Optimization and Control, [MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG], Contraction (operator theory), Mathematics, 010102 general mathematics, 16. Peace & justice, Optimal control, 53C17, 49J15, [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], symbols, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics::Differential Geometry, 010307 mathematical physics |
| الوصف: | We prove comparison theorems for the sub-Riemannian distortion coefficients appearing in interpolation inequalities. These results, which are equivalent to a sub-Laplacian comparison theorem for the sub-Riemannian distance, are obtained by introducing a suitable notion of sub-Riemannian Bakry-\'Emery curvature. The model spaces for comparison are variational problems coming from optimal control theory. As an application we establish the sharp measure contraction property for 3-Sasakian manifolds satisfying a suitable curvature bound. Comment: 37 pages; v2: added section 6.2 on the weighted Heisenberg group, fixed typos. Final version to appear on Mathematische Annalen |
| تدمد: | 1432-1807 0025-5831 |
| DOI: | 10.1007/s00208-020-01982-x |
| DOI: | 10.1007/s00208-020-01982-x⟩ |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8d1108b3e35ac5886e509d7f3de8fd92 https://doi.org/10.1007/s00208-020-01982-x |
| Rights: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....8d1108b3e35ac5886e509d7f3de8fd92 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 14321807 00255831 |
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| DOI: | 10.1007/s00208-020-01982-x |