On Scalar and Ricci Curvatures
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-...
Збережено в:
| Опубліковано в: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2021 |
| ISSN: | 1815-0659 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211303 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On Scalar and Ricci Curvatures. Gerard Besson and Sylvestre Gallot. SIGMA 17 (2021), 046, 42 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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.
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| ISSN: | 1815-0659 |