Related papers: Stability of piecewise flat Ricci flow
The examples of the Ricci flows on four-dimendionsl manifolds which are determined by help of nonlinear differentials equations of the type of Monge-Ampere are constructed. Their particular solutions and their properties are discussed.
We study Ricci flows on $R^n$, $n\ge 3$, that evolve from asymptotically flat initial data. Under mild conditions on the initial data, we show that the flow exists and remains asymptotically flat for an interval of time. The mass is…
We study the existence of solutions of Ricci flow equations of Ollivier-Lin-Lu-Yau curvature defined on weighted graphs. Our work is motivated by\cite{NLLG} in which the discrete time Ricci flow algorithm has been applied successfully as a…
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,…
The 2D Ricci flow equation in the conformal gauge is studied using the linearization approach. Using a non-linear substitution of logarithmic type, the emergent quadratic equation is split in various ways. New special solutions involving…
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…
This article grew out of the urge to realize explicit examples of solutions for the Ricci flow as families of isometrically embedded submanifolds, together with its Gromov-Hausdorff collapses. To this aim, we consider the Ricci flow of…
In this paper, we study the (normalized) Ricci flow on surfaces with conical singularities. Long time existence is proved for cone angle smaller than $2\pi$. In this case, convergence results are obtained if the Euler number is nonpositive.
In this paper we present several curvature estimates for solutions of the Ricci flow which depend on smallness of certain local integrals of the norm of the Riemann curvature tensor.
As part of the general investigation of Ricci flow on complete surfaces with finite total curvature, we study this flow for surfaces with asymptotically conical (which includes as a special case asymptotically Euclidean) geometries. After…
We decribe and announce some results (joint with G. Besson, L. Bessieres, M. Boileau and J.Porti) about the geometry and topology of 3-manifolds. Most of the article is primarily intended as an introduction for nonexperts to geometrization…
In this paper, we study the evolution of L2 p-forms under Ricci flow with bounded curvature on a complete non-compact or a compact Riemannian manifold. We show that under curvature pinching conditions on such a manifold, the L2 norm of a…
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…
The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…
We establish the short-time existence of the Ricci flow on surfaces with a finite number of conic points, all with cone angle between 0 and $2\pi$, where the cone angles remain fixed or change in some smooth prescribed way. For the…
We show that any ancient solution to the Ricci flow which satisfies a suitable curvature pinching condition must have constant sectional curvature.
Recently it has been proved (Lee-Topping 2022, Deruelle-Schulze-Simon 2022, Lott 2019) that three-dimensional complete manifolds with non-negatively pinched Ricci curvature must be flat or compact, thus confirming a conjecture of Hamilton.…
A numerical framework for rigorous linear stability analysis of two-phase stratified flows of two immiscible fluids in horizontal circular pipes is presented. For the first time, three-dimensional disturbances, including those at the…
In this work, we prove uniqueness for complete non-compact Ricci flow with scaling invariant curvature bound. This generalizes the earlier work of Chen-Zhu, Kotschwar and covers most of the example of Ricci flows with unbounded curvature.…
We define the Ricci curvature, as a measure, for certain singular torsion-free connections on the tangent bundle of a manifold. The definition uses an integral formula and vector-valued half-densities. We give relevant examples in which the…