Related papers: Local smooth convergence of $\mathbb{F}$-limit flo…

We introduce the notions of `super-Ricci flows' and `Ricci flows' for time-dependent families of metric measure spaces $(X,d_t,m_t)_{t\in I}$. The former property is proven to be stable under suitable space-time versions of mGH-convergence.…

In this paper we study the evolution of almost non-negatively curved (possibly singular) three dimensional metric spaces by Ricci flow. The non-negatively curved metric spaces which we consider arise as limits of smooth Riemannian manifolds…

In this note, we show that the conical K\"ahler-Ricci flows introduced in \cite{CYW} exist for all time $t\in [0,\infty)$ in the weak sense. As a key ingredient of the proof, we show that a conical K\"ahler-Ricci flow is actually the limit…

We consider the graphical mean curvature flow of strictly area decreasing maps $f:M\to N$, where $M$ is a compact Riemannian manifold of dimension $m>1$ and $N$ a complete Riemannian surface of bounded geometry. We prove long-time existence…

It is a fundamental open problem for the mean curvature flow, and in fact for many partial differential equations, whether or not all blowup limits are selfsimilar. In this short note, we prove that for the mean curvature flow of mean…

In this paper we consider the Ricci flow on manifolds with boundary with appropriate control on its mean curvature and conformal class. We obtain higher order estimates for the curvature and second fundamental form near the boundary,…

In this paper we study a boundary value problem for the Ricci flow in the two dimensional ball endowed with a rotationally symmetric metric. We show short and long time existence results. We construct families of metrics for which the flow…

We prove that solutions of a mildly regularized Perona-Malik equation converge, in a slow time scale, to solutions of the total variation flow. The convergence result is global-in-time, and holds true in any space dimension. The proof is…

We study "warped Berger" solutions $\big(\mc S^1\times\mc S^3,G(t)\big)$ of Ricci flow: generalized warped products with the metric induced on each fiber $\{s\}\times\mathrm{SU}(2)$ a left-invariant Berger metric. We prove that this…

In this article we show that generally almost regular flows, introduced by Bamler and Kleiner, in closed 3-manifolds will either go extinct in finite time or flow to a collection of smooth embedded minimal surfaces, possibly with…

We prove the existence of Ricci flow starting from a class of metrics with unbounded curvature, which are doubly-warped products over an interval with a spherical factor pinched off at an end. These provide a forward evolution from some…

We establish a sharp rate of convergence for a free-boundary curve shortening flow in a convex domain in $\mathbb{R}^{2}$ which converges in finite time to a round half-point.

We investigate the properties of the combinatorial Ricci flow for surfaces, both forward and backward -- existence, uniqueness and singularities formation. We show that the positive results that exist for the smooth Ricci flow also hold for…

Let $(M^n,g_0)$ and $(\bar{M}^{n+1},\bar{g})$ be complete Riemannian manifolds with $|\bar{\nabla}^k\bar{Rm}|\le \bar{C}$ for $k \le 2$, and suppose there is an isometric immersion $F_0: M^n \rightarrow \bar{M}^{n+1}$ with bounded second…

This paper is devoted to the study of the evolution of positively curved metrics on the Wallach spaces $SU(3)/T_{\max}$, $Sp(3)/Sp(1)\times Sp(1)\times Sp(1)$, and $F_4/Spin(8)$. We prove that for all Wallach spaces, the normalized Ricci…

In this paper we study $n$-dimensional Ricci flows $(M^n,g(t))_{t\in [0,T)},$ where $T< \infty$ is a potentially singular time, and for which the spatial $L^p$ norm, $p>\frac n 2$, of the scalar curvature is uniformly bounded on $[0,T).$ In…

Let X be a quasiprojective manifold given by the complement of a divisor $\bD$ with normal crossings in a smooth projective manifold $\bX$. Using a natural compactification of $X$ by a manifold with corners $\tX$, we describe the full…

In this paper we study the Ricci flow on surfaces homeomorphic to a cylinder (that is, a product of the circle with a compact interval). We prove longtime existence results, results on the asymptotic behavior of the flow, and we report on…

In this paper, we consider the steady irrotational Euler flows in multidimensional nozzles. The first rigorous proof on the existence and uniqueness of the incompressible flow is provided. Then, we justify the corresponding low Mach number…

The limiting behavior of the normalized K\"ahler-Ricci flow for manifolds with positive first Chern class is examined under certain stability conditions. First, it is shown that if the Mabuchi K-energy is bounded from below, then the scalar…