Related papers: Super Ricci flow for disjoint unions

Combinatorial Ricci flow on an ideally triangulated compact 3-manifold with boundary was introduced by Luo as a 3-dimensional analog of Chow-Luo's combinatorial Ricci flow on a triangulated surface and conjectured to find algorithmically…

In this paper we survey the recent developments of the Ricci flows on complete noncompact K\"{a}hler manifolds and their applications in geometry.

The second author and H. Yin have developed a Ricci flow existence theory that gives a complete Ricci flow starting with a surface equipped with a conformal structure and a nonatomic Radon measure as a volume measure. This led to the…

This is a continuation of the research in [16]. Let $(\overline{M},g_{-1})$ be a closed geodesic $r_0$-ball in the hyperbolic space $(\mathbb{H}^n,g_{-1})$. Let $m\neq1$ be a positive constant. In this paper, we show that for $n\geq3$,…

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.

The fixed points of the generalized Ricci flow are the Bismut Ricci flat metrics, i.e., a generalized metric $(g,H)$ on a manifold $M$, where $g$ is a Riemannian metric and $H$ a closed $3$-form, such that $H$ is $g$-harmonic and…

In this paper, we study the behavior of Ricci flows on compact orbifolds with finite singularities. We show that Perelman's pseudolocality theorem also holds on orbifold Ricci flow. Using this property, we obtain a weak compactness theorem…

The aim of this article is to provide a Liouville theorem for heat equation along ancient super Ricci flow. We formulate such a Liouville theorem under a growth condition concerning Perelman's reduced distance.

In this paper we investigate a kind of generalized Ricci flow which possesses a gradient form. We study the monotonicity of the given function under the generalized Ricci flow and prove that the related system of partial differential…

Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a heat diffusion process and eventually becomes constant everywhere. Ricci flow has demonstrated its great potential by…

This paper investigates the question of stability for a class of Ricci flows which start at possibly non-smooth metric spaces. We show that if the initial metric space is Reifenberg and locally bi-Lipschitz to Euclidean space, then two…

The paper establishes a series of gradient estimates for positive solutions to the heat equation on a manifold $M$ evolving under the Ricci flow, coupled with the harmonic map flow between $M$ and a second manifold $N$. We prove Li-Yau type…

We discuss a natural form of Ricci--flow conjugation between two distinct general relativistic data sets given on a compact $n\geq 3$-dimensional manifold $\Sigma$. We establish the existence of the relevant entropy functionals for the…

We develop a framework inspired by Lauret's "bracket flow" to study the generalized Ricci flow, as introduced by Streets, on discrete quotients of Lie groups. As a first application, we establish global existence on solvmanifolds in…

We will consider a {\it $\tau$-flow}, given by the equation $\frac{d}{dt}g_{ij} = -2R_{ij} + \frac{1}{\tau}g_{ij}$ on a closed manifold $M$, for all times $t\in [0,\infty)$. We will prove that if the curvature operator and the diameter of…

We discuss the Ricci flow on homogeneous 4-manifolds. After classifying these manifolds, we note that there are families of initial metrics such that we can diagonalize them and the Ricci flow preserves the diagonalization. We analyze the…

In this note we study conformal Ricci flow introduced by Arthur Fischer. We use DeTurck's trick to rewrite conformal Ricci flow as a strong parabolic-elliptic partial differential equations. Then we prove short time existences for conformal…

Using a recently developed piecewise flat method, numerical evolutions of the Ricci flow are computed for a number of manifolds, using a number of different mesh types, and shown to converge to the expected smooth behaviour as the mesh…

This project serves to analyze the behavior of Ricci Flow in five dimensional manifolds. Ricci Flow was introduced by Richard Hamilton in 1982 and was an essential tool in proving the Geometrization and Poincare Conjectures. In general,…

We study the Ricci flow of initial metrics which are C^0-perturbations of the hyperbolic metric on H^n. If the perturbation is bounded in the L^2-sense, and small enough in the C^0-sense, then we show the following: In dimensions four and…