Bartnik’s Mass and Hamilton’s Modified Ricci Flow

A Modified Kähler-Ricci Flow

In this note, we study a Kähler-Ricci flow modified from the classic version. In the non-degenerate case, strong convergence at infinite time is achieved. The main focus should be on degenerate case, where some partial results are presented. 1 Set-up and Motivation Kähler-Ricci flow, which is nothing but Ricci flow with initial metric being Kähler, enjoys the same debut as Ricci flow in R. Hami...

Mass Under the Ricci Flow

In this paper, we study the change of the ADM mass of an ALE space along the Ricci flow. Thus we first show that the ALE property is preserved under the Ricci flow. Then, we show that the mass is invariant under the flow in dimension three (similar results hold in higher dimension with more assumptions). A consequence of this result is the following. Let (M, g) be an ALE manifold of dimension n...

On the Convergence of a Modified Kähler-Ricci Flow

We study the convergence of a modified Kähler-Ricci flow defined by Zhou Zhang. We show that the flow converges to a singular metric when the limit class is degenerate. This proves a conjecture of Zhang.

Ricci Lower Bound for Kähler–ricci Flow

Ricci flow and black holes

Gradient flow in a potential energy (or Euclidean action) landscape provides a natural set of paths connecting different saddle points. We apply this method to General Relativity, where gradient flow is Ricci flow, and focus on the example of 4-dimensional Euclidean gravity with boundary S1 × S2, representing the canonical ensemble for gravity in a box. At high temperature the action has three ...