Turkish Journal of Mathematics
DOI
-
Abstract
This article relies on [15] that the author wrote with Gang Tian and Xiaodong Wang. In view of Hamilton's important work on the Ricci flow and Perelman's paper on the Ricci flow where he developes the techniques that he will later use in completing Hamilton's program for the geometrization conjecture, there may be more interest in the area. We will also discuss the author's theorem which says that the curvature tensor stays uniformly bounded under the unnormalized Ricci flow in a finite time, if the curvatures are uniformly bounded. We will prove that in the case of a Kähler-Ricci flow with uniformly bounded Ricci curvatures, for each sequence of flows g(t_i + t) for t_i \to \infty there exists a subsequence of metrics converging to a solution to the flow outside a set of codimension 4.
Keywords
Ricci flow, smooth convergence
First Page
11
Last Page
22
Recommended Citation
SESUM, NATASA (2004) "Perelman's Monotonicity Formula and Applications," Turkish Journal of Mathematics: Vol. 28: No. 1, Article 2. Available at: https://journals.tubitak.gov.tr/math/vol28/iss1/2
