Related papers: Width and finite extinction time of Ricci flow

A lattice based method will be presented for numerical investigations of Ricci flow. The method will be applied to the particular case of 2-dimensional axially symmetric initial data on manifolds with S^2 topology. Results will be presented…

We prove a curvature pinching result for the Ricci flow on asymptotically flat manifolds: if an asymptotically flat manifold of dimension $n\geq 3$ has scale-invariant integral norm of curvature sufficiently pinched relative to the inverse…

The geometric description of incompressible hydrodynamics, as geodesic motion on the infinite-dimensional group of volume-preserving diffeomorphisms, enables notions of curvature in the study of fluids in order to study stability. Formulas…

Based on the framework of Koch-Lamm and tensor heat kernel estimates, we obtain a uniform proof of the short-time existence, uniqueness, and continuous dependence for Ricci flows starting from a complete Riemannian metric with bounded…

We consider the Kaehler-Ricci flow on complete finite-volume metrics that live on the complement of a divisor in a compact Kaehler manifold X. Assuming certain spatial asymptotics on the initial metric, we compute the singularity time in…

Using an analogue of Myers' theorem for minimal surfaces and three dimensional topology, we prove the diameter sphere theorem for Ricci curvature in dimension three and a corresponding eigenvalue pinching theorem. This settles these two…

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…

Given an asymptotically conical, shrinking, gradient Ricci soliton, we show that there exists a Ricci flow solution on a closed manifold that forms a finite-time singularity modeled on the given soliton. No symmetry or Kahler assumptions on…

Let $\{g(t)\}_{t\in [0,T)}$ be the solution of the Ricci flow on a closed Riemannian manifold $M^n$ with $n\geq 3$. Without any assumption, we derive lower volume bounds of the form ${\rm Vol}_{g(t)}\geq C (T-t)^{\frac{n}{2}}$, where $C$…

In this paper, we study the Ricci flow on manifolds with boundary. In the first part of the paper, we prove short-time existence and uniqueness of the solution, in which the boundary becomes instantaneously umbilic for positive time. In the…

We investigate the limiting behavior of the unnormalized Kahler-Ricci flow on a Kahler manifold with a polarized initial Kahler metric. We prove that the Kahler-Ricci flow becomes extinct in finite time if and only if the manifold has…

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…

This paper studies the Ricci flow on closed manifolds admitting harmonic spinors. It is shown that Perelman's Ricci flow entropy can be expressed in terms of the energy of harmonic spinors in all dimensions, and in four dimensions, in terms…

Let $(M,g)$ be a compact manifold with Ricci curvature almost bounded from below and $\pi:\bar{M}\to M$ be a normal, Riemannian cover. We show that, for any nonnegative function $f$ on $M$, the means of $f\o\pi$ on the geodesic balls of…

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…

We analyse Ricci flow (normalised/un-normalised) of product manifolds --unwarped as well as warped, through a study of generic examples. First, we investigate such flows for the unwarped scenario with manifolds of the type $\mathbb…

We study noncommutative Ricci flow in a finite dimensional representation of a noncommutative torus. It is shown that the flow exists and converges to the flat metric. We also consider the evolution of entropy and a definition of scalar…

This paper attempts to construct monotonic entropy functionals for four-dimensional Lorentzian spacetime under physical boundary conditions, as an extension of Perelman's monotonic entropy functionals constructed for three-dimensional…

We formulate and solve the existence problem for Ricci flow on a Riemann surface with initial data given by a Radon measure as volume measure. The theory leads us to a large class of new examples of nongradient expanding Ricci solitons,…

This is the second part of a series of papers analyzing the long-time behaviour of 3 dimensional Ricci flows with surgery. We generalize the methods developed in the first part and use them to treat cases in which the initial manifold…