A Comparison Theorem and A Sharp Bound via the Ricci Flow

We prove a comparison theorem for the compact surfaces with negative Euler characteristic via the Ricci flow.

A Class of Monotonic Quantities along the Ricci Flow

We construct a class of monotonic quantities along the normalized Ricci flow on closed n-dimensional manifolds.

Some Asymptotic Behavior of the first Eigenvalue along the Ricci Flow

We study some asymptotic behavior of the first nonzero eigenvalue of the Lalacian along the normalized Ricci flow and give a direct short proof for an asymptotic upper limit estimate.