Rigidity of cones with bounded Ricci curvature

Erbar M, Sturm K-T (2021)
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY 23(1): 219-235.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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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 L-2-transport distance. Moreover, we establish rigidity results of independent interest which characterize the N-dimensional standard sphere S-N as the unique minimizer e.g. of integral(X)integral(X) cos(d(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
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
Band
23
Ausgabe
1
Seite(n)
219-235
ISSN
1435-9855
Page URI
https://pub.uni-bielefeld.de/record/2950685

Zitieren

Erbar M, Sturm K-T. Rigidity of cones with bounded Ricci curvature. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. 2021;23(1):219-235.
Erbar, M., & Sturm, K. - T. (2021). Rigidity of cones with bounded Ricci curvature. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 23(1), 219-235. doi:10.4171/JEMS/1010
Erbar, M., and Sturm, K. - T. (2021). Rigidity of cones with bounded Ricci curvature. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY 23, 219-235.
Erbar, M., & Sturm, K.-T., 2021. Rigidity of cones with bounded Ricci curvature. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 23(1), p 219-235.
M. Erbar and K.-T. Sturm, “Rigidity of cones with bounded Ricci curvature”, JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, vol. 23, 2021, pp. 219-235.
Erbar, M., Sturm, K.-T.: Rigidity of cones with bounded Ricci curvature. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. 23, 219-235 (2021).
Erbar, Matthias, and Sturm, Karl-Theodor. “Rigidity of cones with bounded Ricci curvature”. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY 23.1 (2021): 219-235.

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