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-...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2021
Hauptverfasser: Besson, Gerard, Gallot, Sylvestre
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2021
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/211303
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:On Scalar and Ricci Curvatures. Gerard Besson and Sylvestre Gallot. SIGMA 17 (2021), 046, 42 pages

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
Beschreibung
Zusammenfassung: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.
ISSN:1815-0659