相关论文: Revisiting ancient noncollapsed flows in $\mathbb{…

In this paper we introduce a new geometric flow with rotational invariance and prove that, under this kind of flow, an arbitrary smooth closed contractible hypersurface in the Euclidean space Rn+1 (n, 1) converges to Sn in the C1-topology…

We prove the existence of closed convex ancient solutions to curvature flows which become more and more oval for large negative times. The speed function is a general symmetric function of the principal curvatures, homogeneous of degree…

In this paper we prove the convergence of a nonlocal version of the Cahn-Hilliard equation to its local counterpart as the nonlocal convolution kernel is scaled using suitable approximations of a Dirac delta in a periodic boundary…

In this paper we build Non-singular Morse-Smale flows on S^3 with unknotted and unlinked saddle orbits by identifying fat round handles along their boundaries. This way of building the flows enables to get their phase portraits. We also…

The Chern-Ricci flow is an evolution equation of Hermitian metrics by their Chern-Ricci form, first introduced by Gill. Building on our previous work, we investigate this flow on complex surfaces. We establish new estimates in the case of…

We prove that the only closed, embedded ancient solutions to the curve shortening flow on $\mathbb{S}^2$ are equators or shrinking circles, starting at an equator at time $t=-\infty$ and collapsing to the north pole at time $t=0$. To obtain…

Consider a continuous flow in $\mathbb{R}^3$ or any orientable $3$-manifold. Let $(Q_1, Q_0)$ be an index pair in the sense of Conley and consider the region $N := \overline{Q_1 - Q_0}$. (An example of this is a compact $3$-manifold $N$…

This paper is a review of recent results on integrable nonholonomic geodesic flows of left--invariant metrics and left- and right--invariant constraint distributions on compact Lie groups.

This note is a continuation of [CMZ21]. We shall show that an ancient Ricci flow with uniformly bounded Nash entropy must also have uniformly bounded $\nu$-functional. Consequently, on such an ancient solution there are uniform logarithmic…

In this article, we prove two "global existence and full convergence theorems" for flow lines of the M\"obius-invariant Willmore flow, and we use these results, in order to prove that fully and smoothly convergent flow lines of the…

We prove a comparison theorem for the compact surfaces with negative Euler characteristic via the Ricci flow.

We study the Ricci flow for initial metrics with positive isotropic curvature (strictly PIC for short). In the first part of this paper, we prove new curvature pinching estimates which ensure that blow-up limits are uniformly PIC in all…

We present an asymptotic theory for analytical characterization of the high-Reynolds-number incompressible flow of a Newtonian fluid past a shear-free circular cylinder. The viscosity-induced modifications to this flow are localized and…

In this paper we give a new proof, valid for all dimensions, of the classical Herglotz-Noether theorem that all rotational shear-free and expansion-free flows (rotational Born-rigid flows) in Minkowski spacetime are generated by Killing…

The paper provides a different proof of the result of Brendle-Schoen on the differential sphere theorem. It is shown directly that the invariant cone of curvature operators with positive (or non-negative) complex sectional curvature is…

We study ancient Ricci flows which admit asymptotic solitons in the sense of Perelman. We prove that the asymptotic solitons must coincide with Bamler's tangent flows at infinity. Furthermore, we show that Perelman's $\nu$-functional is…

We extend some results known for the K\"ahler-Ricci flow to the Chern-Ricci flow regarding the independence of singularity types for long-time solutions. Specifically, we show that if a solution to the Chern-Ricci flow exists with uniformly…

We exhibit a concentration-collapse decomposition of singularities of fourth order curvature flows, including the $L^2$ curvature flow and Calabi flow, in dimensions $n \leq 4$. The proof requires the development of several new a priori…

Several theories for weakly damped free-surface flows have been formulated. In this paper we use the linear approximation to the Navier-Stokes equations to derive a new set of equations for potential flow which include dissipation due to…

We consider families of strongly indefinite systems of elliptic PDE and investigate bifurcation from a trivial branch of solutions by using the spectral flow. The novelty in our approach is a refined version of a comparison principle that…