5 citations · 6 across the 3 of their papers we have counts for
4 papers
Positivity of Ricci curvature under the Kähler--Ricci flow
Dan Knopf
For all complex dimensions n>=2, we construct complete Kaehler manifolds of bounded curvature and non-negative Ricci curvature whose Kaehler--Ricci evolutions immediately acquire R…
A lower bound for the diameter of solutions to the Ricci flow with nonzero
Tom Ilmanen, Dan Knopf
We obtain a lower bound for the diameter of a solution to the Ricci flow on a compact manifold with nonvanishing first real cohomology. A consequence of our result is an affirmativ…
Hamilton's injectivity radius estimate for sequences with almost nonnegative curvature operators
Bennett Chow, Dan Knopf, Peng Lu
We give a new and complete proof of Hamilton's injectivity radius estimate for sequences with bounded and almost nonnegative curvature operators, unbounded diameters, and bump-like…
New Li--Yau--Hamilton Inequalities for the Ricci Flow via the Space-time Approach
Bennett Chow, Dan Knopf
We generalize Hamilton's matrix Li-Yau-type Harnack estimate for the Ricci flow by considering the space of all LYH (Li-Yau-Hamilton) quadratics that arise as curvature tensors of…