Related papers: A nonexistence result for rotating mean curvature …
Recently a new no-global-recollapse argument was given for some inhomogeneous and anisotropic cosmologies that utilizes surface deformation by the mean curvature flow. In this paper we discuss important properties of the mean curvature flow…
This paper concerns the inverse mean curvature flow of convex hypersurfaces which are Lipschitz in general. After defining a weak solution, we study the evolution of the singularity by looking at the blow-up tangent cone around each…
This work considers the question of whether mean-curvature flow can be modified to avoid the formation of singularities. We analyze the finite-elements discretization and demonstrate why the original flow can result in numerical instability…
We study curvature flows in the locally homogeneous case (e.g. compact quotients of Lie groups, solvmanifolds, nilmanifolds) in a unified way, by considering a generic flow under just a few natural conditions on the broad class of…
In [5], S\'aez and Schn\"urer studied the graphical mean curvature flow of complete hypersurfaces defined on subsets of Euclidean space. They obtained long time existence. Moreover, they provided a new interpretation of weak mean curvature…
Surfaces that evolve by mean curvature flow develop singularities. These singularities can be modeled by self-shrinkers, surfaces that shrink by dilations under the flow. Singularities modeled on classical self-shrinkers, namely spheres and…
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…
We consider the normalized Ricci flow evolving from an initial metric which is conformally compactifiable and asymptotically hyperbolic. We show that there is a unique evolving metric which remains in this class, and that the flow exists up…
In this paper we prove a compactness result for Ricci flows with bounded scalar curvature and entropy. It states that given any sequence of such Ricci flows, we can pass to a subsequence that converges to a metric space which is smooth away…
We consider the flow of closed convex hypersurfaces in Euclidean space $\mathbb{R}^{n+1}$ with speed given by a power of the $k$-th mean curvature $E_k$ plus a global term chosen to impose a constraint involving the enclosed volume…
In this short note we show that non-negative Ricci curvature is not preserved under Ricci flow for closed manifolds of dimensions four and above, strengthening a previous result of Knopf in \cite{K} for complete non-compact manifolds of…
We establish the short-time existence of the Ricci flow on surfaces with a finite number of conic points, all with cone angle between 0 and $2\pi$, where the cone angles remain fixed or change in some smooth prescribed way. For the…
By carrying out a point-wise estimate for the second fundamental form, we prove a rigidity theorem of complete noncompact ancient solutions to the mean curvature flow in codimension one. Moreover, we derive an optimal growth condition.
This article is devoted to the study of an incompressible viscous flow of a fluid partly enclosed in a cylindrical container with an open top surface and driven by the constant rotation of the bottom wall. Such type of flows belongs to a…
It is shown by Colding and Minicozzi the uniqueness of the tangent cone at infinity of Ricci-flat manifolds with Euclidean volume growth which has at least one tangent cone at infinity with a smooth cross section. In this article we raise…
In 1998 Smoczyk [Smo98] showed that, among others, the blowup limits at singularities are convex for the mean curvature flow starting from a closed star-shaped surface in $\mathbf{R}^3$. We prove in this paper that this is true for the mean…
We study the decay of high-Reynolds number Taylor-Couette turbulence, i.e. the turbulent flow between two coaxial rotating cylinders. To do so, the rotation of the inner cylinder (Re$_i=2 \times 10^6$, the outer cylinder is at rest) is…
We construct a rotationally invariant Ricci flow through surgery starting at any closed rotationally invariant Riemannian manifold. We demonstrate that a sequence of such Ricci flows with surgery converges to a Ricci flow spacetime in the…
In this paper we consider a Ricci de Turck flow of spaces with isolated conical singularities, which preserves the conical structure along the flow. We establish that a given initial regularity of Ricci curvature is preserved along the…
We construct new examples of self-translating surfaces for the mean curvature flow from a periodic configuration with finitely many grim reaper cylinders in each period. Because this work is an extension of the author's article on the…