Abstract
In this paper we analyze the behavior of the distance function under Ricci flows whose scalar curvature is uniformly bounded. We will show that on small time-intervals the distance function is \(\frac{1}{2}\)-Hölder continuous in a uniform sense. This implies that the distance function can be extended continuously up to the singular time.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bamler, R., Zhang, Q.: Heat kernel and curvature bounds in Ricci flows with bounded scalar curvature (2015). arXiv:1501.01291
Colding, T.H., Naber, A.: Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications. Ann. Math. 176(2), 1173–1229 (2012). https://doi.org/10.4007/annals.2012.176.2.10
Chen, X., Wang, B.: On the conditions to extend Ricci flow (III). Int. Math. Res. Not. 10, 2349–2367 (2013)
Perelman, G.: The entropy formula for the Ricci flow and its geometric applications (2002). arXiv:math/0211159
Zhang, Q.S.: Bounds on volume growth of geodesic balls under Ricci flow. Math. Res. Lett. 19(1), 245–253 (2012). https://doi.org/10.4310/MRL.2012.v19.n1.a19
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by A. Neves.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Bamler, R.H., Zhang, Q.S. Heat kernel and curvature bounds in Ricci flows with bounded scalar curvature—Part II. Calc. Var. 58, 49 (2019). https://doi.org/10.1007/s00526-019-1484-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00526-019-1484-5