Related papers: Uniqueness and stability of Ricci flow through sin…

We introduce singular Ricci flows, which are Ricci flow spacetimes subject to certain asymptotic conditions. We consider the behavior of Ricci flow with surgery starting from a fixed initial compact Riemannian 3-manifold, as the surgery…

The Ricci flow is a natural evolution equation for Riemannian metrics on a given manifold. The main goal is to understand singularity formation. In his spectacular 2002 breakthrough, Perelman achieved a qualitative understanding of…

Let $(M,g_0)$ be a compact $n$-dimensional Riemannian manifold with a finite number of singular points, where the metric is asymptotic to a non-negatively curved cone over $(\mathbb{S}^{n-1},g)$. We show that there exists a smooth Ricci…

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.

In this short note, we observe that the Bamler-Kleiner proof of uniqueness and stability for 3-dimensional Ricci flow through singularities generalizes to singular Ricci flows in higher dimensions that satisfy an analogous canonical…

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 extend the concept of singular Ricci flow by Kleiner and Lott from 3d compact manifolds to 3d complete manifolds with possibly unbounded curvature. As an application of the generalized singular Ricci flow, we show that for any 3d…

We show that an orientable 3-dimensional manifold M admits a complete riemannian metric of bounded geometry and uniformly pos- itive scalar curvature if and only if there exists a finite collection F of spherical space-forms such that M is…

In this survey we provide an overview of our recent results concerning Ricci de Turck flow on spaces with isolated conical singularities. The crucial characteristic of the flow is that it preserves the conical singularity. Under certain…

We prove the short-time existence of Ricci flows on complete manifolds with scalar curvature bounded below uniformly, Ricci curvature bounded below by a negative quadratic function, and with almost Euclidean isoperimetric inequality holds…

We show the existence of a solution to the Ricci flow with a compact length space of bounded curvature, i.e., a space that has curvature bounded above and below in the sense of Alexandrov, as its initial condition. We show that this flow…

In this paper we prove local existence of a Ricci de Turck flow starting at a space with incomplete edge singularities and flowing for a short time within a class of incomplete edge manifolds. We derive regularity properties for the…

We prove that Perelman's ancient ovals occur as blowup limit in 3d Ricci flow through singularities if and only if there is an accumulation of spherical singularities.

In this paper, we are interested in conical structures of manifolds with respect to the Ricci flow and, in particular, we study them from the point of view of Perelman's functionals. In a first part, we study Perelman's $\lambda$ and $\nu$…

In this paper we study the Ricci flow on compact four-manifolds with positive isotropic curvature and with no essential incompressible space form. Our purpose is two-fold. One is to give a complete proof of Hamilton's classification theorem…

We complete the proof of the Generalized Smale Conjecture, apart from the case of $RP^3$, and give a new proof of Gabai's theorem for hyperbolic 3-manifolds. We use an approach based on Ricci flow through singularities, which applies…

We consider a normalization of the Ricci flow on a closed Riemannian manifold given by the evolution equation $\partial_{t}g(t)=-2(Ric(g(t))-\frac{1}{2\tau}g(t))$ where $\tau$ is a fixed positive number. Assuming that a solution for this…

The Ricci flow is an evolution system on metrics. For a given metric as initial data, its local existence and uniqueness on compact manifolds was first established by Hamilton \cite{Ha1}. Later on, De Turck \cite{De} gave a simplified…

In this paper we discuss Perelman's Lambda-functional, Perelman's Ricci shrinker entropy as well as the Ricci expander entropy on a class of manifolds with isolated conical singularities. On such manifolds, a singular Ricci de Turck flow…

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…