Research interests

1. The Heat Kernel Estimate on the Asymptotically Hyperbolic Manifolds and the Stability of the Asymptotically Hyperbolic Einstein Manifolds (joint with Jie Qing)
More details
• Studied the relations between the heat kernel of Lichnerowicz Laplacian and the long time existence and the convergence of the Ricci flow based on the result of R.Bamler .
• Studied the relations between the heat kernel of Lichnerowicz Laplacian and the resolvent of Lichnerowicz Laplacian (This is a direct corollary of the spectrum theorem) and tried to get the estimate of the heat kernel of Lichnerowicz Laplacian by the corresponding Schwartz kernel of that. By the work of X.Chen and A.Hassell, in order to get a good estimate of the heat kernel of of Lichnerowicz Laplacian, we need a tensor version result of R.B.Melrose, A.S.Barreto and A.Vasy.
• Trying to generalized the result of R.B.Melrose, A.S.Barreto, A.Vasy about the Schwartz kernel estimate from the Laplacian operator on the function to the Lichnerowicz Laplacian on the symmetric two tensor.
2. The Perturbation Existence and the stability of Conformally Compact Einstein Manifolds under the Ricci flow (joint with Jie Qing) (A draft of my paper about this result)
• Recovered J. Lee's result (See the Theorem A) about the perturbation Existence of the conformally compact Einstein manifolds by the Ricci flow
• Improved the result of J.Qing, Y.Shi and J.Wu (See Theorem 1.3) about the stability of conformally compact Einstein manifolds.