12 citations · 25 across the 7 of their papers we have counts for
6 papers · 1 filter
Differential Harnack Estimates for Time-dependent Heat Equations with Potentials
Xiaodong Cao, Richard S. Hamilton
In this paper, we prove a differential Harnack inequality for positive solutions of time-dependent heat equations with potentials. We also prove a gradient estimate for the positiv…
On Locally Conformally Flat Gradient Shrinking Ricci Solitons
Xiaodong Cao, Biao Wang, Zhou Zhang
In this paper, we first apply an integral identity on Ricci solitons to prove that closed locally conformally flat gradient Ricci solitons are of constant sectional curvature. We t…
Differential Harnack Estimates for Backward Heat Equations with Potentials under the Ricci Flow
Xiaodong Cao
In this paper, we derive a general evolution formula for possible Harnack quantities. As a consequence, we prove several differential Harnack inequalities for positive solutions of…
Cross Curvature Flow on Locally Homogeneous Three-manifolds (II)
Xiaodong Cao, Laurent Saloff-Coste
In this paper, we study the positive cross curvature flow on locally homogeneous 3-manifolds. We describe the long time behavior of these flows. We combine this with earlier result…
First Eigenvalues of Geometric Operators under the Ricci Flow
Xiaodong Cao
In this paper, we prove that the first eigenvalues of () is nondecreasing under the Ricci flow. We also prove the monotonicity under the normalized flow for…
Cross Curvature Flow on Locally Homogenous Three-manifolds (I)
Xiaodong Cao, Yilong Ni, Laurent Saloff-Coste
Chow and Hamilton introduced the cross curvature flow on closed 3-manifolds with negative or positive sectional curvature. In this paper, we study the negative cross curvature flow…