相关论文: Recent Developments on the Ricci Flow

The recent results on anisotropic flow in ultrarelativistic nuclear collisions along with recent methodical developments and achievements in the understanding of the phenomena, are reviewed. The emphasis is given to the elliptic flow…

We give a simple proof for the rotational symmetry of ancient solutions of Ricci flow on surfaces. As a consequence we obtain a simple proof of some results of P.Daskalopoulos, R.Hamilton and N.Sesum on the a priori estimates for the…

We show that for certain locally collapsing initial data with Ricci curvature bounded below, one could start the Ricci flow for a definite period of time. This provides a Ricci flow smoothing tool, with which we find topological conditions…

Hamilton's pinching conjecture, that three-dimensional complete non-compact manifolds with pinched Ricci curvature are flat, has recently been resolved using Ricci flow. In this paper we prove a direct analogue of that result in all…

We compute the evolution equation of the Weyl tensor under the Ricci flow of a Riemannian manifold and we discuss some consequences for the classification of locally conformally flat Ricci solitons.

In this thesis we give a review on Ricci flow, an overview on Poincare conjecture, maximum principle, Li-Yau-Perelman estimate, Two functional F and W of Perelman, Reduced volume and reduced length and k-non collapsing estimate

In this paper, we will recover Hamilton's Harnack inequality for the Ricci flow from the view point of Hyperbolic thermostat.

This paper shows for the first time the existence of a Ricci flow with surgery with local topology change \mathbb{CP}^2\setminus\{ \mathrm{pt}\} \rightarrow \mathbb{R}^4. The post surgery flow converges to the Taub-NUT metric on…

We give a global picture of the Ricci flow on the space of three-dimensional, unimodular, nonabelian metric Lie algebras considered up to isometry and scaling. The Ricci flow is viewed as a two-dimensional dynamical system for the evolution…

In this work we construct and analyze exact solutions describing Ricci flows and nonholonomic deformations of four dimensional (4D) Taub-NUT spacetimes. It is outlined a new geometric techniques of constructing Ricci flow solutions. Some…

We construct a uniform local bound of curvature operator from local bounds of Ricci curvature and injectivity radius among all $n$-dimensional Ricci flows. Thus new compactness theorems for the Ricci flow and Ricci solitons are derived. In…

We review some of the recent developments in QCD spin physics and highlight the spin program now underway at RHIC.

In this paper, we provide an essentially self-contained and detailed account of the fundamental works of Hamilton and the recent breakthrough of Perelman on the Ricci flow and their application to the geometrization of three-manifolds. In…

We prove the convergence of K\"ahler-Ricci flow with some small initial curvature conditions. As applications, we discuss the convergence of K\"ahler-Ricci flow when the complex structure varies on a K\"ahler-Einstein manifold.

In this work, we study gradient solitons to general geometric flows. Our approach is to understand what assumptions need to be made about a flow in order to extend results about Ricci solitons. In this direction, we identify an identity,…

We use the Ricci flow with surgery to study four-dimensional SU(2) x U(1)-symmetric metrics on a manifold with fixed boundary given by a squashed 3-sphere. Depending on the initial metric we show that the flow converges to either the…

In this article, we establish a monotonicity formula of Hamilton type entropy along Ricci flow on compact surfaces with boundary. We also study the relation between our entropy functional and the $\mathcal{W}$-functional of Perelman type.

In this paper we prove a compactness result for Ricci flows with bounded scalar curvature and entropy. It states that given any sequence of such Ricci flows, we can pass to a subsequence that converges to a metric space which is smooth away…

We prove results relating the theory of optimal transport and generalized Ricci flow. We define an adapted cost functional for measures using a solution of the associated dilaton flow. This determines a formal notion of geodesics in the…

We introduce the new notion of Bianchi-convex sets, a generalization of convex sets of algebraic curvature tensors inspired by the second Bianchi identity. It turns out that Hamilton's maximum principle for the Ricci flow can be generalized…