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A generalization of Hamilton's differential Harnack inequality for the Ricci flow
S. Brendle
In [10], R. Hamilton established a differential Harnack inequality for solutions to the Ricci flow with nonnegative curvature operator. We show that this inequality holds under the…
A general convergence result for the Ricci flow in higher dimensions
S. Brendle
Let (M,g_0) be a compact Riemannian manifold of dimension n \geq 4. We show that the normalized Ricci flow deforms g_0 to a constant curvature metric provided that (M,g_0) x R has…
Classification of manifolds with weakly 1/4-pinched curvatures
S. Brendle, R. M. Schoen
We show that a compact Riemannian manifold with weakly 1/4-pinched sectional curvatures is either locally symmetric or diffeomorphic to a space form.
Manifolds with 1/4-pinched Curvature are Space Forms
S. Brendle, R. M. Schoen
Let (M,g_0) be a compact Riemannian manifold with pointwise 1/4-pinched sectional curvatures. We show that the Ricci flow deforms g_0 to a constant curvature metric. The proof uses…