Related papers: Monotonicity and Kaehler-Ricci flow

We show some computations related to the motion by mean curvature flow of a submanifold inside an ambient Riemannian manifold evolving by Ricci or backward Ricci flow. Special emphasis is given to the possible generalization of Huisken's…

In this paper we reconcile several different approaches to Ricci flow through singularities that have been proposed over the last few years by Kleiner-Lott, Haslhofer-Naber and Bamler. Specifically, we prove that every noncollapsed limit of…

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…

The Ricci flow was introduced by Hamilton and gained its importance through the years. Of special importance is the limiting behavior of the flow and its symmetry properties. Taking this into account, we present a novel normalization for…

In this paper we study non-singular solutions of Ricci flow on a closed manifold of dimension at least 4. Amongst others we prove that, if M is a closed 4-manifold on which the normalized Ricci flow exists for all time t>0 with uniformly…

Let $X = M \times E$ where $M$ is an $m$-dimensional K\"ahler manifold with negative first Chern class and $E$ is an $n$-dimensional complex torus. We obtain $C^\infty$ convergence of the normalized K\"ahler-Ricci flow on $X$ to a…

We derive identities for general flows of Riemannian metrics that may be regarded as local mean-value, monotonicity, or Lyapunov formulae. These generalize previous work of the first author for mean curvature flow and other nonlinear…

We develop a parabolic pluripotential theory on compact K{\"a}hler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge-Amp{\`e}re equations. We provide a parabolic analogue of the celebrated Bedford-Taylor…

We improve the understanding of both finite time and infinite time singularities of the modified K\"ahler-Ricci flow as initiated by the second author of this paper in [26]. This is done by relating the modified K\"ahler-Ricci flow with the…

We rigorously show that a large family of monotone quantities along the weak inverse mean curvature flow is the limit case of the corresponding ones along the level sets of $p$-capacitary potentials. Such monotone quantities include…

We show that for any solvable Lie group of real type, any homogeneous Ricci flow solution converges in Cheeger-Gromov topology to a unique non-flat solvsoliton, which is independent of the initial left-invariant metric. As an application,…

We consider the K\"ahler-Ricci flow $(X, \omega(t))_{t \in [0,T)}$ on a compact manifold where the time of singularity, $T$, is finite. We assume the existence of a holomorphic map from the K\"ahler manifold $X$ to some analytic variety $Y$…

In this paper we study a generalization of the Kahler-Ricci flow, in which the Ricci form is twisted by a closed, non-negative (1,1)-form. We show that when a twisted Kahler-Einstein metric exists, then this twisted flow converges…

The main purpose of this note is to construct two functionals of the positive solutions to the conjugate heat equation associated to the metrics evolving by the conformal Ricci flow on closed manifolds. We show that they are nondecreasing…

The famous Uniformization Theorem states that on closed Riemannian surfaces there always exists a metric of constant curvature for the Levi-Cevita connection. In this article we prove that an analogue of the uniformization theorem also…

The main goal of this paper is to prove $L^1$-comparison and contraction principles for weak solutions (in the sense of distributions) of Hele-Shaw flow with a linear Drift. The flow is considered with a general reaction term including the…

In this paper we will give a new proof of the monotonicity of Wasserstein distances of two diffusions under super Ricci flow. Our proof is based on the coupling method of B.Andrew and J.Clutterbuck. The same method can also be applied to…

We consider classical solutions to $-\Delta u = f(u)$ in half-spaces, under homogeneous Dirichlet boundary conditions. We prove that any positive solution is strictly monotone increasing in the direction orthogonal to the boundary, provided…

We complement a recent work on the stability of fixed points of the CMC-Einstein-$\Lambda$ flow. In particular, we modify the utilized gauge for the Einstein equations and remove a restriction on the fixed points whose stability we are able…

We investigate Riemannian (non-Kahler) Ricci flow solutions that develop finite-time Type-I singularities and present evidence in favor of a conjecture that parabolic rescalings at the singularities converge to singularity models that are…