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-...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2021 |
| 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| _version_ | 1862531242971365376 |
|---|---|
| author | Besson, Gerard Gallot, Sylvestre |
| author_facet | Besson, Gerard Gallot, Sylvestre |
| citation_txt | On Scalar and Ricci Curvatures. Gerard Besson and Sylvestre Gallot. SIGMA 17 (2021), 046, 42 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-12T13:20:41Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211303 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-12T13:20:41Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Besson, Gerard Gallot, Sylvestre 2025-12-29T11:06:15Z 2021 On Scalar and Ricci Curvatures. Gerard Besson and Sylvestre Gallot. SIGMA 17 (2021), 046, 42 pages 1815-0659 2020 Mathematics Subject Classification: 51K10; 53C23; 53C21; 53E20; 57K30 arXiv:2010.08207 https://nasplib.isofts.kiev.ua/handle/123456789/211303 https://doi.org/10.3842/SIGMA.2021.046 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Scalar and Ricci Curvatures Article published earlier |
| spellingShingle | On Scalar and Ricci Curvatures Besson, Gerard Gallot, Sylvestre |
| title | On Scalar and Ricci Curvatures |
| title_full | On Scalar and Ricci Curvatures |
| title_fullStr | On Scalar and Ricci Curvatures |
| title_full_unstemmed | On Scalar and Ricci Curvatures |
| title_short | On Scalar and Ricci Curvatures |
| title_sort | on scalar and ricci curvatures |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211303 |
| work_keys_str_mv | AT bessongerard onscalarandriccicurvatures AT gallotsylvestre onscalarandriccicurvatures |