Related papers: On the properties of the combinatorial Ricci flow …
In this paper, we continue to study the generalized Ricci flow. We give a criterion on steady gradient Ricci soliton on complete and noncompact Riemannian manifolds that is Ricci-flat, and then introduce a natural flow whose stable points…
In the present work we find the Lie point symmetries of the Ricci flow on an $n$-dimensional manifold. and we introduce a method in order to reutilize these symmetries to obtain the Lie point symmetries of particular metrics. We apply this…
In this work, we use the Ricci flow approach to study the gap phenomenon of Riemannian manifolds with non-negative curvature and sub-critical scaling invariant curvature decay. The first main result is a quantitative Ricci flow existence…
In his seminal work \cite{Ri96}, Rivin characterized finite ideal polyhedra in three-dimensional hyperbolic space. However, the characterization of infinite ideal polyhedra, as proposed by Rivin, has remained a long-standing open problem.…
Given a completely arbitrary surface, whether or not it has bounded curvature, or even whether or not it is complete, there exists an instantaneously complete Ricci flow evolution of that surface that exists for a specific amount of time…
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 show that the distance function under the Ricci flow is uniformly continuous in the time direction, assuming only the scalar curvature is bounded.
In [12], the existence of ideal circle patterns in Euclidean or hyperbolic background geometry under the combinatorial conditions was proved using flow approaches. It remains as an open problem for the spherical case. In this paper, we…
In this paper, for a given compact 3-manifold with an initial Riemannian metric and a symmetric tensor, we establish the short-time existence and uniqueness theorem for extension of cross curvature flow. We give an example of this flow on…
In this note we clarify that the Rcci flow can be used to give an independent proof of the uniformization theorem of Riemann surfaces.
The Ricci flow on the 2-sphere with marked points is shown to converge in all three stable, semi-stable, and unstable cases. In the stable case, the flow was known to converge without any reparametrization, and a new proof of this fact is…
We introduce a new class of discrete conformal structures on surfaces with boundary, which have nice interpolations in 3-dimensional hyperbolic geometry. Then we prove the global rigidity of the new discrete conformal structures using…
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…
We study the combinatorial Calabi flow for ideal circle patterns in both hyperbolic and Euclidean background geometry. We prove that the flow exists for all time and converges exponentially fast to an ideal circle pattern metric on surfaces…
This paper is concerned with properties of maximal solutions of the Ricci and cross curvature flows on locally homogeneous three-manifolds of type SL(2,R). We prove that, generically, a maximal solution originates at a sub-Riemannian…
Motivated by the Hamilton's Ricci flow, we define the homogeneous flow of a parallelizable manifold and show the long time existence and uniqueness of its solutions on $[0,\infty).$ Using this flow, we outline a simple proof of the Poincare…
In this paper we survey the recent developments of the Ricci flows on complete noncompact K\"{a}hler manifolds and their applications in geometry.
In this paper, we give a sufficient condition such that the Ricci flow in $R^2$ exists globally and the flow converges at $t=\infty$ to the flat metric on $R^2$.
In this note we prove the backwards uniqueness of the mean curvature flow for (codimension one) hypersurfaces in a Euclidean space. More precisely, let $F_t, \widetilde{F}_t:M^n \rightarrow \mathbb{R}^{n+1}$ be two complete solutions of the…