Related papers: Evolving hypersurfaces by their inverse null mean …
In this paper, we study the regularized mean curvature flow starting from invariant hypersurfaces in a Hilbert space equipped with an isometric almost free Hilbert Lie group action whose orbits are minimal regularizable submanifolds, where…
Given a compact four dimensional smooth Riemannian manifold $(M,g)$ with smooth boundary, we consider the evolution equation by $Q$-curvature in the interior keeping the $T$-curvature and the mean curvature to be zero and the evolution…
In this paper, we first study the behavior of inverse mean curvature flow in Schwarzschild manifold. We show that if the initial hypersurface $\Sigma$ is strictly mean convex and star-shaped, then the flow hypersurface $\Sigma_t$ converges…
In this paper, we study the existence, uniqueness and asymptotic behavior of rotationally symmetric translating solitons of the mean curvature flow in Minkowski space. We also study the asymptotic behavior and the strict convexity of…
We consider strictly convex hypersurfaces which are evolving by the non-parametric logarithmic Gauss curvature flow subject to a Neumann boundary condition. Solutions are shown to converge smoothly to hypersurfaces moving by translation. In…
Given any nondegenerate k-dimensional minimal submanifold K of codimension greater than 1, we prove the existence of families of constant mean curvature submanifolds, with mean curvature varying from one member of the family to another,…
In [8] Gerhardt proves longtime existence for the inverse mean curvature flow in globally hyperbolic Lorentzian manifolds with compact Cauchy hypersurface, which satisfy three main structural assumptions: a strong volume decay condition, a…
In a recent paper, Eichmair, Galloway and Pollack have proved a Gannon-Lee-type singularity theorem based on the existence of marginally outer trapped surfaces (MOTS) on noncompact initial data sets for globally hyperbolic spacetimes. This…
We show some computations related to the motion by mean curvature flow of a submanifold inside an ambient Riemannian manifold evolving by Ricci or backward Ricci flow. Special emphasis is given to the possible generalization of Huisken's…
We provide the first general result for the asymptotics of the area preserving mean curvature flow in two dimensions showing that flat flow solutions, starting from any bounded set of finite perimeter, converge with exponential rate to a…
In a recent paper, Eichmair, Galloway and Pollack have proved a Gannon-Lee-type singularity theorem based on the existence of marginally outer trapped surfaces (MOTS) on noncompact initial data sets for globally hyperbolic spacetimes.…
Motivated by the conjectured Penrose inequality and by the work of Hawking, Geroch, Huisken and Ilmanen in the null and the Riemannian case, we examine necessary conditions on flows of two-surfaces in spacetime under which the Hawking…
The main result of this paper is a convexity estimate for translating solitons of extrinsic geometric flows which evolve under a $1$-homogeneous concave function in the principal curvatures. In addition, we show examples of these…
We study the mean curvature flow of complete space-like submanifolds in pseudo-Euclidean space with bounded Gauss image, as well as that of complete submanifolds in Euclidean space with convex Gauss image. By using the confinable property…
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…
The skew mean curvature flow(SMCF), which origins from the study of fluid dynamics, describes the evolution of a codimension two submanifold along its binormal direction. We study the basic properties of the SMCF and prove the existence of…
We study the contraction of strictly convex, axially symmetric hypersurfaces by a non-symmetric, non-homogeneous, fully nonlinear function of curvature. Starting from axially symmetric hypersurfaces with even profile curves, we show…
In this paper, we investigate the mean curvature flow having equifocal submanifolds as initial data. The investigation are performed by investigating the mean curvature flow having the lifted submanifolds to a Hilbert space through a…
We consider the generalized evolution of compact level sets by functions of their normal vectors and second fundamental forms on a Riemannian manifold M. The level sets of a function $u:M\to\mathbb{R}$ evolve in such a way whenever u solves…
We study one-parameter curves on the universal Teichm\"uller space $T$ and on the homogeneous space $M=\Diff S^1/\Rot S^1$ embedded into $T$. As a result, we deduce evolution equations for conformal maps that admit quasiconformal extensions…