Related papers: On homogeneous Ricci solitons
In this paper, we extend the theory of Ricci flows satisfying a Type-I scalar curvature condition at a finite-time singularity. In [Bam16], Bamler showed that a Type-I rescaling procedure will produce a singular shrinking gradient Ricci…
In this paper we study 4d gradient steady Ricci solitons, which are weak $\kappa$-solutions, and admit O(3)-symmetry. Under a weak curvature decay condition, we find precise geometric asymptotics of such solitons, which are similar to those…
Ancient solutions arise in the study of Ricci flow singularities. Motivated by the work of Fateev on 3-dimensional ancient solutions we construct high dimensional ancient solutions to Ricci flow on spheres and complex projective spaces as…
We show the existence of expanding solitons of the G$_2$-Laplacian flow on non-solvable Lie groups, and we give the first example of a steady soliton that is not an extremally Ricci pinched G$_2$-structure.
In this paper we study certain types of metrics such as Ricci soliton, $*$-conformal Ricci soliton in 3-dimensional trans-Sasakian manifold. First we have shown that a 3-dimensional trans-Sasakian manifold of type $(\alpha,\beta)$ admits a…
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…
This paper introduce the idea of second Ricci solitons. A second Ricci soliton is nothing but a steady hyperbolic Ricci soliton. We study the geometry of closed and compact second Ricci soliton manifolds. Immersed submanifolds as second…
This is a revised version of our short note [arxiv.math.DG/0403065] where we discuss the monotonicity of the eigen-values of the Laplacian operator to the Ricci-Hamilton flow on a compact or a complete non-compact Riemannian manifold. We…
On a hyperbolic 3-manifold of finite volume, we prove that if the initial metric is sufficiently close to the hyperbolic metric $h_0$, then the normalized Ricci-DeTurck flow exists for all time and converges exponentially fast to $h_0$ in a…
We prove the uniqueness of solutions of the Ricci flow on complete noncompact manifolds with bounded curvatures using the De Turck approach. As a consequence we obtain a correct proof of the existence of solution of the Ricci harmonic flow…
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…
In this paper we study the evolution of almost non-negatively curved (possibly singular) three dimensional metric spaces by Ricci flow. The non-negatively curved metric spaces which we consider arise as limits of smooth Riemannian manifolds…
We describe the structure of the Ricci tensor on a locally homogeneous Lorentzian gradient Ricci soliton. In the non-steady case, we show the soliton is rigid in dimensions three and four. In the steady case, we give a complete…
We confirm a conjecture of Hamilton: On compact manifolds the normalized Ricci flow evolves metrics with positive curvature operators to limit metrics with constant curvature.
We study the Ricci flow on $\mathbb{R}^{n+1}$, with $n\geq 2$, starting at some complete bounded curvature rotationally symmetric metric $g_{0}$. We first focus on the case where $(\mathbb{R}^{n+1},g_{0})$ does not contain minimal…
We analyse some properties of the cohomogeneity one Ricci soliton equations, and use Ansatze of cohomogeneity one type to produce new explicit examples of complete Kahler Ricci solitons of expanding, steady and shrinking types. These…
In this paper, we study the asymptotic geometry of a noncollapsed ancient Ricci flow with nonnegative Ricci curvature via its tangent flow at infinity -- a noncollapsed $\mathbb{F}$-limit metric soliton [Bam23,CMZ23]. We first prove some…
The stability of a recently developed piecewise flat Ricci flow is investigated, using a linear stability analysis and numerical simulations, and a class of piecewise flat approximations of smooth manifolds is adapted to avoid an inherent…
In this article, we study geometric and analytical features of complete noncompact $\rho$-Einstein solitons, which are self-similar solutions of the Ricci-Bourguignon flow. We study the spectrum of the drifted Laplacian operator for…
In this announcement, we exhibit the second variation of Perelman's $\lambda$ and $\nu$ functionals for the Ricci flow, and investigate the linear stability of examples. We also define the "central density" of a shrinking Ricci soliton and…