题目: Heat kernel estimate and regularity of Ricci-harmonic flow
摘要:In this talk we discuss Ricci-harmonic flow on which the scalar curvature is bounded. At first, we establish a time derivative bound for solution to the heat equation, based on this, we derive the distance distortion estimate and the existence of a cutoff function. At last we use these to get the heat kernel upper bound and lower bound along Ricci-harmonic flow. Moreover, we can derive the backward pseudolocality Theorem along this flow. As applications, we obtain the L^2 bound of the Riemannian curvature in four dimension.
Part of the work is joint with Prof Yi Li.