Related papers: An Elementary Remark on a Lower bound for the $\mu…
In this note, we provide some general discussion on the Ricci lower bound along K\"ahler-Ricci flow with singularity over closed manifold.
Until recently, Ricci flow was viewed almost exclusively as a way of deforming Riemannian metrics of bounded curvature. Unfortunately, the bounded curvature hypothesis is unnatural for many applications, but is hard to drop because so many…
We prove sharp lower bounds for eigenvalues of the drift Laplacian for a modified Ricci flow. The modified Ricci flow is a system of coupled equations for a metric and weighted volume that plays an important role in Ricci flow. We will also…
In this paper we present several curvature estimates for solutions of the Ricci flow which depend on smallness of certain local integrals of the norm of the Riemann curvature tensor.
In this short note, we give simple proof of the Ricci flow's local existence and uniqueness on closed Einstein manifolds. We suggest a new setting for studying the space of Riemannian metrics on a compact manifold.
I survey some of the developments in the theory of Ricci flow and its applications from the past decade. I focus mainly on the understanding of Ricci flows that are permitted to have unbounded curvature in the sense that the curvature can…
We establish a short-time existence theory for complete Ricci flows under scaling-invariant curvature bounds, starting from rotationally symmetric metrics on $\mathbb{R}^{n+1}$ that are noncollapsed at infinity, without assuming bounded…
Some modification of the old version.In this note we give a proof of a result which is related to Perelman's theorem in Section 10.3 of the paper "The entropy formula for the Ricci flow and its geometric applications".
We establish several quantitative results about singular Ricci flows, including estimates on the curvature and volume, and the set of singular times.
In this paper we prove the existence of Type II singularities for the Ricci flow on $S^{n+1}$ for all $n\geq 2$.
We present two new conditions to extend the Ricci flow on a compact manifold over a finite time, which are improvements of some known extension theorems.
We consider the Ricci flow for simply connected nilmanifolds, which translates to a Ricci flow on the space of nilpotent metric Lie algebras. We consider the evolution of the inner product and the evolution of structure constants, as well…
We derive, under a technical assumption, the first variation formula for the eigenvalues of the Laplacian on a closed manifold evolving by the Ricci flow and give some applications.
In this paper, we study the singularities of two extended Ricci flow systems --- connection Ricci flow and Ricci harmonic flow using newly-defined curvature quantities. Specifically, we give the definition of three types of singularities…
In this paper we study the behavior of the Ricci flow at infinity for the full flag manifold $SU(3)/T$ using techniques of the qualitative theory of differential equations, in special the Poincar\'e Compactification and Lyapunov exponents.…
This article reports recent developments of the research on Hamilton's Ricci flow and its applications.
We discuss some classification results for Ricci solitons, that is, self similar solutions of the Ricci Flow. Some simple proofs of known results will be presented. In detail, we will take the equation point of view, trying to avoid the…
This is the first of a series of papers, where we introduce a new class of estimates for the Ricci flow, and use them both to characterize solutions of the Ricci flow and to provide a notion of weak solutions to the Ricci flow in the…
If we want to deform a compact Riemannian manifold with boundary using Ricci flow, we first need to decide on appropriate boundary conditions. We would like these conditions to reflect the geometric nature of the flow and allow for a…
In this short notes, we discuss monotonicity formulas under various rescaled versions of Ricci flow. The main result is Theorem \ref{theo rescaled}.