Curvature Diffusion of Inverse-weight Lin--Lu--Yau Ricci Flow on Finite Trees

Abstract: We study the continuous Lin--Lu--Yau Ricci flow on a finite tree in the inverse-weight case. We investigate the diffusive structure of the curvature evolution equation and prove the convergence of the curvature along the Ricci flow. Moreover, we show that, in logarithmic coordinates, the Ricci flow can be characterized as the gradient flow of a convex potential.