Related papers: Monotonicity and Kaehler-Ricci flow

We show that the singularities of the twisted K\"ahler--Einstein metric arising as the long-time solution of the K\"ahler--Ricci flow or in the collapsed limit of Ricci-flat K\"ahler metrics is intimately related to the holomorphic…

Inspired by work of Besson-Courtois-Gallot, we construct a flow called the natural flow on a non-positively curved Riemannian manifold $M$. As with the natural map, the $k$-Jacobian of the natural flow is directly related to the critical…

We offer a simple and self-contained proof that the Follow-the-Leader model converges to the Lighthill-Whitham-Richards model for traffic flow.

We find explicit solutions and singularities of the Ricci-harmonic flow of $\mathrm{G_2}$-structures, the Ricci-like flows of $\mathrm{G_2}$-structures studied by Gianniotis-Zacharopoulos in arXiv:2505.06872 (J. Geom. Anal. 36.2 (2026)) and…

B List has proposed a geometric flow whose fixed points correspond to solutions of the static Einstein equations of general relativity. This flow is now known to be a certain Hamilton-DeTurck flow (the pullback of a Ricci flow by an…

We introduce a class of flows on the Wasserstein space of probability measures with finite first moment on the Cartan-Hadamard Riemannian manifold of positive definite matrices, and consider the problem of differentiability of the…

Under suitable conditions near infinity and assuming boundedness of curvature tensor, we prove a no breathers theorem in the spirit of Ivey-Perelman for some noncompact Ricci flows. These include Ricci flows on asymptotically flat (AF)…

We introduce a novel curvature flow, the Heterotic-Ricci flow, as the two-loop renormalization group flow of the Heterotic string common sector and study its three-dimensional compact solitons. The Heterotic-Ricci flow is a coupled…

In dimension $n=3$, there is a complete theory of weak solutions of Ricci flow - the singular Ricci flows introduced by Kleiner and Lott - which are unique across singularities, as was proved by Bamler and Kleiner. We show that uniqueness…

We study the Ricci flow for the Lorentzian Einstein-Hilbert action. We show that Einstein gravity emerges as a fixed point of the Einstein-Ricci flow equations and derive a renormalization group flow in Euclidean signature. By considering…

We prove an estimate for solutions to the linearized Ricci flow system on closed 3-manifolds. This estimate is a generalization of Hamilton's pinching is preserved estimate for the Ricci curvatures of solutions to the Ricci flow on…

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 show that the twisted K\"ahler-Ricci flow on a complex manifold X converges to a flow of moving free boundaries, in a certain scaling limit. This leads to a new phenomenon of singularity formation and topology change which can be seen as…

This is a revised version of our short note [arxiv.math.DG/0403065] where we discuss the monotonicity of the eigen-values of the Laplacian operator to the Ricci-Hamilton flow on a compact or a complete non-compact Riemannian manifold. We…

Let $(M,J_0)$ be a Fano manifold which admits a K\"ahler-Ricci soliton, we analyze the behavior of the K\"ahler-Ricci flow near this soliton as we deform the complex structure $J_0$. First, we will establish an inequality of Lojasiewicz's…

We give a geometric interpretation of Hamilton's matrix Harnack inequality for the Ricci flow as the curvature of a connection on space-time.

On a Fano manifold, we prove that the Kahler-Ricci flow starting from a Kahler metric in the anti-canonical class which is sufficiently close to a Kahler-Einstein metric must converge in a polynomial rate to a Kahler-Einstein metric. The…

Following work of Ecker, we consider a weighted Gibbons-Hawking-York functional on a Riemannian manifold-with-boundary. We compute its variational properties and its time derivative under Perelman's modified Ricci flow. The answer has a…

The paper establishes a series of gradient estimates for positive solutions to the heat equation on a manifold $M$ evolving under the Ricci flow, coupled with the harmonic map flow between $M$ and a second manifold $N$. We prove Li-Yau type…

We introduce a new continuity method which provides an alternative way of carrying out the Analytic Minimal Model Program introduced by G. Tian and J. Song and G. Tian. This equation -- unlike the Ricci flow -- has the advantage of having…