On Scalar and Ricci Curvatures
| العنوان: | On Scalar and Ricci Curvatures |
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| المؤلفون: | Sylvestre Gallot, Gérard Besson |
| المساهمون: | Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA) |
| المصدر: | Symmetry, Integrability and Geometry : Methods and Applications Symmetry, Integrability and Geometry : Methods and Applications, National Academy of Science of Ukraine, 2021, ⟨10.3842/SIGMA.2021.046⟩ |
| بيانات النشر: | SIGMA (Symmetry, Integrability and Geometry: Methods and Application), 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, Pure mathematics, metric spaces, Group Theory (math.GR), [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], Whitehead 3-manifolds, Mathematics - Metric Geometry, Ricci flow, volume entropy, FOS: Mathematics, scalar curvature, [MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG], metric measured space, Mathematical Physics, Ricci curvature, Mathematics, Bishop–Gromov inequality, Busemann spaces, Whitehead manifold, Bishop-Gromov inequality, Metric Geometry (math.MG), Volume entropy, Metric space, hyperbolic groups, Differential Geometry (math.DG), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], Bounded function, Metric (mathematics), Gromov-hyperbolic spaces, 51K10, 53C21, 20F65, synthetic Ricci curvature, Mathematics::Differential Geometry, Geometry and Topology, infinite connected sums, Bishop-Gromov's Inequality, Mathematics - Group Theory, Analysis, Scalar curvature |
| الوصف: | The purpose of this report is to acknowledge the influence of M. Gromov's vision of geometry on our own works. It is two-fold: in the first part we aim at describing some results, in dimension 3, around the question: which open 3-manifolds carry a complete Riemannian metric of positive or non negative scalar curvature? In the second part we look for weak forms of the notion of ''lower bounds of the Ricci curvature'' on non necessarily smooth metric measure spaces. We describe recent results some of which are already posted in [arXiv:1712.08386] where we proposed to use the volume entropy. We also attempt to give a new synthetic version of Ricci curvature bounded below using Bishop-Gromov's inequality. |
| تدمد: | 1815-0659 |
| الوصول الحر: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f6d2b059f5699f59ebbad90c37fc3874Test https://doi.org/10.3842/sigma.2021.046Test |
| حقوق: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....f6d2b059f5699f59ebbad90c37fc3874 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 18150659 |
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