Related papers: Pseudo-locality for a coupled Ricci flow

We present local estimates for solutions to the Ricci flow, without the assumption that the solution has bounded curvature. These estimates lead to a generalisation of one of the pseudolocality results of G.Perelman in dimension two.

We develop a refined singularity analysis for the Ricci flow by investigating curvature blow-up rates locally. We first introduce general definitions of Type I and Type II singular points and show that these are indeed the only possible…

A framework of quantum spacetime reference frame is proposed and reviewed, in which the quantum spacetime at the Gaussian approximation is deformed by the Ricci flow. At sufficient large scale, the Ricci flow not only smooths out local…

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…

We derive a family of weighted scalar curvature monotonicity formulas for generalized Ricci flow, involving an auxiliary dilaton field evolving by a certain reaction-diffusion equation motivated by renormalization group flow. These scalar…

We study blow-ups around fixed points at Type I singularities of the Ricci flow on closed manifolds using Perelman's W-functional. First, we give an alternative proof of the result obtained by Naber and Enders-M\"{u}ller-Topping that…

In this article we prove an $\epsilon$-regularity theorem for non-collapsed Ricci flows, and use this to prove new estimates for singularity models of Fano K\"ahler-Ricci flows. In the course of our proof, we find a criterion for uniform…

We prove a pseudolocality type theorem for compact Ricci Flow under local integral bounds of curvature. The main tool is Local Ricci Flow introduced by Deane Yang in [4] and Pseudolocality Theorem of Perelman in [3]. We also study L^p…

We prove that the Ricci flow on CP^n blown-up at one point starting with any rotationally symmetric Kahler metric must develop Type I singularities. In particular, if the total volume does not go to zero at the singular time, the parabolic…

We define several notions of singular set for Type I Ricci flows and show that they all coincide. In order to do this, we prove that blow-ups around singular points converge to nontrivial gradient shrinking solitons, thus extending work of…

We study the Ricci flow out of spaces with edge type conical singularities along a closed, embedded curve. Under the additional assumption that for each point of the curve, our space is locally modelled on the product of a fixed positively…

Lai (2021) used singular Ricci flows, introduced by Kleiner and Lott (2017), to construct a nonnegative Ricci curvature Ricci flow $g(t)$ emerging from an arbitrary 3D complete noncompact Riemannian manifold $(M^3, g_0)$ which has…

By Perelman's $\mathcal L$-geodesic theory, we study the blow-down solutions on a noncompact $\kappa$-noncollapsed steady gradient Ricci soliton $(M^n, g)$ $(n\ge 4)$ with nonnegative curvature operator and positive Ricci curvature away…

In each dimension $N\geq 3$ and for each real number $\lambda\geq 1$, we construct a family of complete rotationally symmetric solutions to Ricci flow on $\mathbb{R}^{N}$ which encounter a global singularity at a finite time $T$. The…

In this paper we study $n$-dimensional Ricci flows $(M^n,g(t))_{t\in [0,T)},$ where $T< \infty$ is a potentially singular time, and for which the spatial $L^p$ norm, $p>\frac n 2$, of the scalar curvature is uniformly bounded on $[0,T).$ In…

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…

We show that $\kappa$-solutions to the Ricci flow in dimensions $n\geq 4$ whose asymptotic shrinking Ricci soliton is the round cylinder $\mathbb{S}^{n-1}\times\mathbb{R}$ must be uniformly PIC. Combined with earlier classification results,…

In this paper we prove that there is no $\kappa$-solution of Ricci flow on 3-dimensional noncompact manifold with strictly positive sectional curvature and blow up at some finite time $T$ satisfying $\int^T_0 \sqrt{T-t} R(p_0,t)dt< \infty$…

We derive modified Perelman-type monotonicity formulas for solutions to the generalized Ricci flow equation with symmetry on principal bundles, which lead to rigidity and classification results for nonsingular solutions.

In this short note, we prove that the only simply connected noncompact three-dimensional Type I $\kappa$-solution to the Ricci flow is the shrinking cylinder. This work can be regarded as a generalization of Cao and Chow, and a complement…