We show that any complete ancient solution to the Ricci flow equation with possibly unbounded curvature has constant curvature at each time if its curvature is pinched all the time. This is a slight extension of a result of Brendle, Huisken and Sinestrari for ancient solutions on compact manifolds. In our proof, we adapt their argument relying on the maximum principle with the help of Chen’s technique.
ASJC Scopus subject areas
- Statistics and Probability
- Geometry and Topology
- Statistics, Probability and Uncertainty