Abstract
AbstractWe show two sphere theorems for the Riemannian manifolds with scalar curvature bounded below and the non-collapsed $$\mathrm {RCD}(n-1,n)$$
RCD
(
n
-
1
,
n
)
spaces with mean distance close to $$\frac{\pi }{2}$$
π
2
.
Funder
Georg-August-Universität Göttingen
Publisher
Springer Science and Business Media LLC
Reference33 articles.
1. Abresch, U., Meyer, W.T.: Injectivity radius estimates and sphere theorems. In: Comparison Geometry (Berkeley, CA, 1993–94), vol. 30 of Math. Sci. Res. Inst. Publ., pp. 1–47. Cambridge Univ. Press, Cambridge (1997)
2. Brendle, S., Schoen, R.: Sphere theorems in geometry. In: Surveys in Differential Geometry. Vol. XIII. Geometry, Analysis, and Algebraic Geometry: Forty Years of the Journal of Differential Geometry, volume 13 of Surv. Differ. Geom., pp. 49–84. Int. Press, Somerville, MA (2009)
3. Brendle, S., Schoen, R.: Curvature, sphere theorems, and the Ricci flow. Bull. Am. Math. Soc. 48(1), 1–32 (2011)
4. Cheeger, J., Colding, T.H.: On the structure of spaces with Ricci curvature bounded below. I. J. Differ. Geom. 46(3), 406–480 (1997)
5. Chern, S.S., Goldberg, S.I.: On the volume decreasing property of a class of real harmonic mappings. Am. J. Math. 97, 133–147 (1975)