Local pinching estimates in 3-dim Ricci flow
  We study curvature pinching estimates of Ricci flow on complete 3- dimensional manifolds without bounded curvature assumption. We will derive some general curvature conditions which are preserved on any complete solution of 3-dim Ricci flow, these conditions include nonnegative Ricci curvature and sectional curvature as special cases. A local version of Hamilton-Ivey estimates is also obtained. 
Bing-Long Chen, Guoyi Xu, Zhuhong Zhang
math.DG math.AP