相关论文: A solution to Flinn's conjecture on weakly expansi…

We introduce a new geometric flow called the chord shortening flow which is the negative gradient flow for the length functional on the space of chords with end points lying on a fixed submanifold in Euclidean space. As an application, we…

We develop and implement a novel lattice Boltzmann scheme to study multicomponent flows on curved surfaces, coupling the continuity and Navier-Stokes equations with the Cahn-Hilliard equation to track the evolution of the binary fluid…

We provide a connection between weak solution concepts of mean curvature flow. On the one side we have the viscosity solution which is based on the comparison principle. On the other, variational solutions, which are combined Brakke flows…

We consider the obstacle problem of the weak solution for the mean curvature flow, in the sense of Brakke's mean curvature flow. We prove the global existence of the weak solution with obstacles which have $C^{1,1}$ boundaries, in two and…

In his 1979 paper Trotman proves, using the techniques of the Thom transversality theorem, that under some conditions on the dimensions of the manifolds under consideration, openness of the set of maps transverse to a stratification in the…

The author treats the system of motion for an incompressible non-Newtonian fluids of the stress tensor described by $p-$potential function subject to slip boundary conditions in $\mathbb{R}^3_+$. Making use of the Oseen-type approximation…

A kind of problems of radially symmetric transient fluid flow in a medium with a geometry similar to a hollow-disk can be addressed using the finite Hankel transform. However, the inverse Hankel transform [G. Cinelli, Int. J. Engng. Sci.,…

A normalizing flow models a complex probability density as an invertible transformation of a simple density. The invertibility means that we can evaluate densities and generate samples from a flow. In practice, autoregressive flow-based…

In this paper, we study fully nonlinear curvature flows of noncompact spacelike hypersurfaces in Minkowski space. We prove that if the initial hypersurface satisfies certain conditions, then the flow exists for all time. Moreover, we show…

We point out that the geometry of connected totally geodesic compact null hypersurfaces in Lorentzian manifolds is only slightly more specialized than that of Riemannian flows over compact manifolds, the latter mathematical theory having…

A new antidynamo theorem for non-stretched twisted magnetic flux tube dynamo is obtained. Though Riemannian curvature cannot be neglected since one considers curved magnetic flux tube axis, the stretch can be neglect since one only…

We consider the problem of evolving hypersurfaces by mean curvature flow in the presence of obstacles, that is domains which the flow is not allowed to enter. In this paper, we treat the case of complete graphs and explain how the approach…

We study the long time behavior of the Hesse-Koszul flow on compact Hessian manifolds. When the first affine Chern class is negative, we prove that the flow converges to the unique Hesse-Einstein metric. We also derive a convergence result…

We provide a new proof that the horocycle flow preserving the Margulis measure on a variable negative curvature surface is standard. This was first proved by Ratner. The main purpose of this note is to provide a simplified case of the…

A recurring obstacle in the study of Wasserstein gradient flow is the lack of convexity of the square Wasserstein metric. In this paper, we develop a class of transport metrics that have better convexity properties and use these metrics to…

In this article we show that generally almost regular flows, introduced by Bamler and Kleiner, in closed 3-manifolds will either go extinct in finite time or flow to a collection of smooth embedded minimal surfaces, possibly with…

The aim of this work is to prove $C^1$ weak Palis conjecture for nonsingular flows. Weak Palis conjecture claims that a generic vector field either is Morse-Smale or exhibits horseshoes. Central model is come up with by Crovisier to obtain…

We study the dynamics of the geodesic and horocycle flows of the unit tangent bundle $(\hat M, T^1\mathcal{F})$ of a compact minimal lamination $(M,\mathcal F)$ by negatively curved surfaces. We give conditions under which the action of the…

We recall fundamental aspects of the pluriclosed flow equation and survey various existence and convergence results, and the various analytic techniques used to establish them. Building on this, we formulate a precise conjectural…

In this short paper, we give a new proof of the classification theorem for noncompact ancient noncollapsed flows in $\mathbb{R}^3$ originally due to Brendle-Choi (Inventiones 2019). Our new proof directly establishes selfsimilarity by…