Rigidity of cones with bounded Ricci curvature

Erbar M, Sturm K-T (2021)
J. Eur. Math. Soc. (JEMS) 23(1): 219-235.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
OA 170.22 KB
Autor*in
Erbar, MatthiasUniBi; Sturm, Karl-Theodor
Abstract / Bemerkung
We show that the only metric measure space with the structure of an N-cone and with two-sided synthetic Ricci bounds is the Euclidean space RN+1 for N integer. This is based on a novel notion of Ricci curvature upper bounds for metric measure spaces given in terms of the short time asymptotic of the heat kernel in the L2-transport distance. Moreover, we establish rigidity results of independent interest which characterize the N-dimensional standard sphere SN as the unique minimizer of ∫X​∫X​cosd(x,y)m(dy)m(dx) among all metric measure spaces with dimension bounded above by N and Ricci curvature bounded below by N−1.
Stichworte
Metric measure space; synthetic Ricci bounds; rigidity
Erscheinungsjahr
2021
Zeitschriftentitel
J. Eur. Math. Soc. (JEMS)
Band
23
Ausgabe
1
Seite(n)
219-235
ISSN
1435-9855
eISSN
1435-9863
Page URI
https://pub.uni-bielefeld.de/record/2980840

Zitieren

Erbar M, Sturm K-T. Rigidity of cones with bounded Ricci curvature. J. Eur. Math. Soc. (JEMS). 2021;23(1):219-235.
Erbar, M., & Sturm, K. - T. (2021). Rigidity of cones with bounded Ricci curvature. J. Eur. Math. Soc. (JEMS), 23(1), 219-235. https://doi.org/10.4171/jems/1010
Erbar, Matthias, and Sturm, Karl-Theodor. 2021. “Rigidity of cones with bounded Ricci curvature”. J. Eur. Math. Soc. (JEMS) 23 (1): 219-235.
Erbar, M., and Sturm, K. - T. (2021). Rigidity of cones with bounded Ricci curvature. J. Eur. Math. Soc. (JEMS) 23, 219-235.
Erbar, M., & Sturm, K.-T., 2021. Rigidity of cones with bounded Ricci curvature. J. Eur. Math. Soc. (JEMS), 23(1), p 219-235.
M. Erbar and K.-T. Sturm, “Rigidity of cones with bounded Ricci curvature”, J. Eur. Math. Soc. (JEMS), vol. 23, 2021, pp. 219-235.
Erbar, M., Sturm, K.-T.: Rigidity of cones with bounded Ricci curvature. J. Eur. Math. Soc. (JEMS). 23, 219-235 (2021).
Erbar, Matthias, and Sturm, Karl-Theodor. “Rigidity of cones with bounded Ricci curvature”. J. Eur. Math. Soc. (JEMS) 23.1 (2021): 219-235.
Alle Dateien verfügbar unter der/den folgenden Lizenz(en):
Creative Commons Namensnennung 4.0 International Public License (CC-BY 4.0):
Volltext(e)
Access Level
OA Open Access
Zuletzt Hochgeladen
2024-01-23T08:38:34Z
MD5 Prüfsumme
619626464f2f96d0d177ce85fb041e3d


Link(s) zu Volltext(en)
Access Level
OA Open Access

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®
Suchen in

Google Scholar