A geometric proof of the classification of complex vector cross product
In this article, we give a geometric proof of the classification of complex vector cross product due to Lee-Leung.
math.DG↗
arXiv subjects
Chengjie Yu
Publications and source records attributed to Chengjie Yu.
Negativity of Perelman's Li-Yau-Hamilton type expression
Chau-Tam-Yu has proved the non-positivity of Perelman's new Li-Yau-Hamilton type expression on noncompact manifolds. In this article, we further prove that $v$ is negative if the Ricci flow is not end up with an Euclidean space.
math.DG↗
Some Estimates of Fundamental Solution on noncompact manifolds with time-dependent metrics
In this article, we obtain some further estimates of fundamental solutions comparing to the result of Chau-Tam-Yu and give some applications of the estimates on asymptotic behaviors of fundamental solutions.
math.DG↗
Pseudolocality for the Ricci flow and applications
In \cite{P1}, Perelman established a differential Li-Yau-Hamilton (LYH) type inequality for fundamental solutions of the conjugate heat equation corresponding to the Ricci flow on compact manifolds (also see \cite{N2}). As an application of the LYH inequality, Perelman proved a pseudolocality result for the Ricci flow on compact manifolds. In this article we provide the details for the proofs of these results in the case of a complete non-compact Riemannian manifold. Using these results we prove that under certain conditions, a finite time singularity of the Ricci flow must form within a compact set. We also prove a long time existence result for the \KRF flow on complete non-negatively curved \K manifolds.
math.DG↗