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-...

Повний опис

Збережено в:
Бібліографічні деталі
Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2021
Автори: Besson, Gerard, Gallot, Sylvestre
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2021
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/211303
Теги: Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
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.
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