Related papers: On the weak K\"ahler-Ricci flow
We survey some recent work using Ricci flow to create a class of local definitions of weak lower scalar curvature bounds that is well defined for $C^0$ metrics. We discuss several properties of these definitions and explain some…
We report a direct-numerical-simulation study of Taylor-Couette flow in the quasi-Keplerian regime at shear Reynolds numbers up to $\mathcal{O}(10^5)$. Quasi-Keplerian rotating flow has been investigated for decades as a simplified model…
We give a geometric interpretation of the linear trace Harnack inequality for the Ricci flow.
In recent years, there are many progress made in K\"ahler geometry. In particular, the topics related to the problems of the existence and uniqueness of extremal K\"ahler metrics, as well as obstructions to the existence of such metrics in…
We study an analogue of the Calabi flow in the non-K\"ahler setting for compact Hermitian manifolds with vanishing first Bott-Chern class. We prove a priori estimates for the evolving metric along the flow given a uniform bound on the Chern…
We study some asymptotic behavior of the first nonzero eigenvalue of the Lalacian along the normalized Ricci flow and give a direct short proof for an asymptotic upper limit estimate.
For a Fano manifold, We consider the geometric quantization of the K\"ahler-Ricci flow and the associated entropy functional. Convergence to the original flow and entropy is established. It is also possible to formulate the…
This note illustrates the Ricci flow method based on the Cao.H.D's paper[1] and Yau.S.T's paper[4], and tries to explain the method in detail, especially in some calculations. Jian Song and Weinkove's note[9] used some other estimates to…
This is a survey on the Strominger system and a geometric flow known as the anomaly flow. We will discuss various aspects of non-K\"ahler geometry on Calabi-Yau threefolds. Along the way, we discuss balanced metrics and balanced classes,…
Ricci flow on two dimensional surfaces is far simpler than in the higher dimensional cases. This presents an opportunity to obtain much more detailed and comprehensive results. We review the basic facts about this flow, including the…
In this paper, we study the class of Finsler metrics, namely (\alpha, \beta)- metrics, which satisfies the un-normal or normal Ricci flow equation.
We consider the Cauchy problem for incompressible viscoelastic fluids in the whole space $\mathbb{R}^d$ ($d=2,3$). By introducing a new decomposition via Helmholtz's projections, we first provide an alternative proof on the existence of…
The flow of an electrically conducting fluid in a thin disc under the action of an azimuthal Lorentz force is studied experimentally. At small forcing, the Lorentz force is balanced by either viscosity or inertia, yielding quasi-Keplerian…
In this paper, we consider the $V$-soliton equation which is a degenerate fully nonlinear equation introduced by La Nave and Tian in their work on K\"ahler-Ricci flow on symplectic quotients. One can apply the interpretation to study finite…
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…
In this paper, we show that the singularity type of solutions to the K\"aher-Ricci flow on a numerically effective manifold does not depend on the initial metric. More precisely if there exists a type III solution to the K\"ahler-Ricci…
We give a maximum principle proof of interior derivative estimates for the K\"ahler-Ricci flow, assuming local uniform bounds on the metric.
We consider an abstract functional-differential equation derived from the pressure-less Euler system with variable coefficients that includes several systems of partial differential equations arising in the fluid mechanics. Using the method…
We show anomalous dissipation of scalars advected by weak solutions to the incompressible Euler equations with $C^{(\sfrac{1}{3})^-}$ regularity, for an arbitrary initial datum in $\dot H^1 (\T^3)$. This is the first rigorous derivation of…
In this paper we prove that a nonflat K\"{a}hler-Ricci soliton of the Ricci flow on a complex two-dimensional K\"{a}hler manifold with nonnegative holomorphic bisectional curvature can not be of maximal volume growth.