Related papers: Ricci flow on asymptotically Euclidean manifolds

Let $F$ be a left invariant Randers metric on a simply connected nilpotent Lie group $N$, induced by a left invariant Riemannian metric ${\hat{\textbf{\textit{a}}}}$ and a vector field $X$ which is…

Chau-Tam-Yu has proved the non-positivity of Perelman's new Li-Yau-Hamilton type expression on noncompact manifolds. In this article, we further prove that $v$ is negative if the Ricci flow is not end up with an Euclidean space.

In this paper, we study the Ricci flow on a closed manifold and finite time interval $[0,T)~(T < \infty)$ on which certain integral curvature energies are finite. We prove that in dimension four, such flow converges to a smooth Riemannian…

We study the Ricci flow on $\mathbb{R}^{n+1}$, with $n\geq 2$, starting at some complete bounded curvature rotationally symmetric metric $g_{0}$. We first focus on the case where $(\mathbb{R}^{n+1},g_{0})$ does not contain minimal…

Let $(M,g(t))$, $0\le t\le T$, be a n-dimensional complete noncompact manifold, $n\ge 2$, with bounded curvatures and metric $g(t)$ evolving by the Ricci flow $\frac{\partial g_{ij}}{\partial t}=-2R_{ij}$. We will extend the result of L. Ma…

In this article, we study complete Type I ancient Ricci flows with positive sectional curvature. Our main results are as follows: in the complete and noncompact case, all such ancient solutions must be noncollapsed on all scales; in the…

We show uniqueness of Ricci flows starting at a surface of uniformly negative curvature, with the assumption that the flows become complete instantaneously. Together with the more general existence result proved in [10], this settles the…

We consider the Ricci flow equation for invariant metrics on compact and connected homogeneous spaces whose isotropy representation decomposes into two irreducible inequivalent summands. By studying the corresponding dynamical system, we…

In this paper, we study Ricci flow on compact manifolds with a continuous initial metric. It was known from Simon that the Ricci flow exists for a short time. We prove that the scalar curvature lower bound is preserved along the Ricci flow…

We study a class of non-smooth asymptotically flat manifolds on which metrics fails to be $C^1$ across a hypersurface $\Sigma$. We first give an approximation scheme to mollify the metric, then we prove that the Positive Mass Theorem still…

Let $(M,g)$ be a complete noncompact non-collapsing $n$-dimensional riemannian manifold, whose complex sectional curvature is bounded from below and scalar curvature is bounded from above. Then ricci flow with above as its initial data, has…

We show that for a broad family of noncompact homogeneous Riemannian manifolds, the corresponding homogeneous Ricci flow solutions have finite extinction time, thereby confirming the dynamical Alekseevskii conjecture for these spaces. As an…

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 announce a new proof of the uniform estimate on the curvature of solutions to the Ricci flow on a compact K\"ahler manifold $M^n$ with positive bisectional curvature. In contrast to the recent work of X. Chen and G. Tian, our proof of…

In this note we study conformal Ricci flow introduced by Arthur Fischer. We use DeTurck's trick to rewrite conformal Ricci flow as a strong parabolic-elliptic partial differential equations. Then we prove short time existences for conformal…

We show for a non homogeneous boundary value problem for the Ricci flow on the disk that when the initial metric has positive curvature and the boundary is convex then the initial metric is deformed, via the normalized flow and along…

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…

In this paper, we focus on Hamilton's pinching conjecture formulated in Hamilton's paper "Three-manifolds with positive Ricci curvature". Let $(M, g)$ be a complete, connected, noncompact Riemannian $3$-manifold satisfying the…

We prove that Ricci flows with almost maximal extinction time must be nearly round, provided that they have positive isotropic curvature when crossed with $\mathbb{R}^{2}$. As an application, we show that positively curved metrics on…

We prove that for any complete n-dimensional Riemannian manifold with nonnegative Ricci curvature, if the Nash inequality is satisfied, then it is diffeomorphic to $R^{n}$l.