相关论文: Local curvature estimates for the Laplacian flow

We address in this paper the study of a geometric evolution, corresponding to a curvature which is non-local and singular at the origin. The curvature represents the first variation of the energy recently proposed as a variant of the…

Local structures, beyond the well-known `frozen-in' to the barotropic flows of the generalized vorticities, of the two-fluid model of plasma flows are presented. More general non-barotropic situations are also considered. A modified Euler…

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 prove new variation formulae for the volume of coassociative submanifolds, expressed in terms of $G_2$ data. As a special case, we obtain a second variation formula for variations within the moduli space of coassociative submanifolds;…

We use a first-order energy quantity to prove a strengthened statement of uniqueness for the Ricci flow. One consequence of this statement is that if a complete solution on a noncompact manifold has uniformly bounded Ricci curvature, then…

This is the second part of a series of papers analyzing the long-time behaviour of 3 dimensional Ricci flows with surgery. We generalize the methods developed in the first part and use them to treat cases in which the initial manifold…

In this paper, we introduce a kind of inverse mean curvature flow (1.2) in a Sasakian sub-Riemannian 3-manifold $M$ for Legendrian curves, which slightly differs from the classical one, and confirm that this flow preserves the Legendrian…

In this note, we establish a local maximum principle along Ricci flow under scaling invariant curvature condition. This unifies the known preservation of nonnegativity results along Ricci flow with unbounded curvature. By combining with the…

We introduce a notion of uniform convergence for local and nonlocal curvatures. Then, we propose an abstract method to prove the convergence of the corresponding geometric flows, within the level set formulation. We apply such a general…

In this paper, we construct solutions of Lagrangian mean curvature flow which exist and are embedded for all time, but form an infinite-time singularity and converge to an immersed special Lagrangian as $t\to\infty$. In particular, the flow…

For a general $k$-dimensional Brakke flow in $\mathbb{R}^n$ locally close to a $k$-dimensional plane in the sense of measure, it is proved that the flow is represented locally as a smooth graph over the plane with estimates on all the…

We prove that the restricted holonomy group of a complete smooth solution to the Ricci flow of uniformly bounded curvature cannot spontaneously contract in finite time; it follows, then, from an earlier result of Hamilton that the holonomy…

Expressions for G-dot are considered in a multidimensional model with an Einstein internal space and a multicomponent perfect fluid. In the case of two non-zero curvatures without matter, a mechanism for prediction of small G-dot is…

In this paper we study the local regularity of closed surfaces immersed in a Riemannian 3-manifold flowing by Willmore flow. We establish a pair of concentration-compactness alternatives for the flow, giving a lower bound on the maximal…

In this note, we obtain a sharp volume estimate for complete gradient Ricci solitons with scalar curvature bounded below by a positive constant. Using Chen-Yokota's argument we obtain a local lower bound estimate of the scalar curvature for…

In this paper, we investigate the prescribed curvature problem associated with a special Lin-Lu-Yau curvature on finite graphs of girth at least 6. We define the corresponding Calabi flow for this curvature type, and establish an equivalent…

In this paper, we investigate the Cauchy problem associated to a system of PDE's of Oldroyd type. The considered model describes the evolution of certain viscoelastic fluids within a corotational framework. The non-corotational setting is…

Let $(M,g)$ be a complete noncompact non-collapsing $n$-dimensional riemannian manifold, whose complex sectional curvature is bounded from below and scalar curvature is bounded from above. Then ricci flow with above as its initial data, has…

We study a new notion of Ricci curvature that applies to Markov chains on discrete spaces. This notion relies on geodesic convexity of the entropy and is analogous to the one introduced by Lott, Sturm, and Villani for geodesic measure…

In this paper, we study the evolution of metrics on finite trees under continuous-time Ricci flows based on the Lin-Lu-Yau version of Ollivier Ricci curvature. We analyze long-time dynamics of edge weights and curvatures, providing precise…