Long-time behavior of Ricci flow on some complex surfaces
John Lott
本文通过双Lipschitz模型研究了某些4维流形（一般型极小曲面）上Ricci流的长时间行为，展示了膨胀与静态行为的结合。
我们给出了某些4维流形（一般型极小曲面）上Ricci流的双Lipschitz模型，展示了膨胀与静态行为的结合。
We give biLipschitz models for the Ricci flow on some 4-manifolds (minimal surfaces of general type), exhibiting a combination of expanding and static behavior.
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We extend the concept of singular Ricci flow by Kleiner and Lott from 3d compact manifolds to 3d complete manifolds with possibly unbounded curvature. As an application of the generalized singular Ricci flow, we show that for any 3d complete Riemannian manifold with non-negative Ricci curvature, there exists a smooth Ricci flow starting from it.
In this note, we provide some general discussion on the Ricci lower bound along Kähler-Ricci flow with singularity over closed manifold.
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Ancient Ricci flows with nonnegative Ricci curvature
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Parabolic frequency monotonicity on Ricci flow and Ricci-harmonic flow with bounded curvatures
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We prove that for any complete three-manifold with a lower Ricci curvature bound and a lower bound on the volume of balls of radius one, a solution to the Ricci flow exists for short time. Actually our proof also yields a (non-canonical) way to flow and regularize some interior region of a non-complete initial data satisfying the aformentioned bounds.
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On the dynamical behaviour of the generalized Ricci flow
本文将Müller-Haslhofer关于Ricci流下Ricci平坦度量动力学稳定性与不稳定性的结果推广到广义Ricci流，得到了Ricci平坦度量与消失3-形式配对的相应动力学稳定性与不稳定性结论。
Here, we study the existence and uniqueness of solutions to the Ricci flow on Finsler surfaces and show short time existence of solutions for such flows. To this purpose, we first study the Finslerian Ricci-DeTurck flow on Finsler surfaces and find a unique short time solution to this flow. Then, we find a solution to the original Ricci flow by pulling back the solution of the Ricci-DeTurck flow using appropriate diffeomorphisms. In the end, we illustrate this argument with some examples.
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In this paper, we will recover Hamilton's Harnack inequality for the Ricci flow from the view point of Hyperbolic thermostat.
We prove that the scalar curvature of a homogeneous Ricci flow solution blows up at a forward or backward finite-time singularity.
In this paper we present our results on the logarithmic Sobolev inequality along the Ricci flow in dimension 2.
A short proof of the convergence of the Kahler-Ricci flow on Fano manifolds admitting a Kahler-Einstein metric or a Kahler-Ricci soliton is given, using a variety of recent techniques
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In this paper we survey the recent developments of the Ricci flows on complete noncompact Kähler manifolds and their applications in geometry.
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We introduce the notion of Canonical Expanding Ricci Soliton, and use it to derive new Harnack inequalities for Ricci flow. This viewpoint also gives geometric insight into the existing Harnack inequalities of Hamilton and Brendle.
In this note, we provide some general discussion on the two main versions in the study of Kahler-Ricci flows over closed manifolds, aiming at smooth convergence to the corresponding Kahler-Einstein metrics with assumptions on the volume form and Ricci curvature form along the flow.
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