相关论文: Invariant $\lambda$-translators in Lorentz-Minkows…

In this paper, we consider translators (for the mean curvature flow) given by a graph of a function on a symmetric space $G/K$ of compact type which is invariant under a hyperpolar action on $G/K$. First, in the case of $G/K=SO(n+1)/SO(n)$,…

In this article we prove two non-existence results for translating solitons of the mean curvature flow (translators for short) in $\mathbb{R}^{m+1}$. We also obtain an upper bound to the maximum height that a compact embedded translator in…

In this paper, we obtain the classification theorem for three-dimensional complete space-like $\lambda$-translators $x:M^{3} \rightarrow \mathbb R^{4}_{1}$ with constant norm of the second fundamental form and constant $f_{4}$ in the…

In this paper, we classify all noncollapsed singularity models for the mean curvature flow of 3-dimensional hypersurfaces in $\mathbb{R}^4$ or more generally in $4$-manifolds. Specifically, we prove that every noncollapsed translating…

In this paper we discuss existence, uniqueness and some properties of a class of solitons to the anisotropic mean curvature flow, i.e., graphical translators, either in the plane or under an assumption of cylindrical symmetry on the…

In this paper we prove existence and classification results for translating solitons defined as initial conditions for higher order mean curvature flows that are invariant by translations in warped product manifolds $\mathbb{P}\times_\chi…

Translators can be regarded as submanifolds which satisfy the mean curvature flow equation when evolving by translations along a distinguished vector field of the ambient space. We study translators in Generalised Robertson-Walker…

In this paper, we study $K^{\alpha}$--translators on parallel surfaces and canal surfaces in 3-dimensional Euclidean space $\mathbb{E}^3$. First, we investigate the condition under which two parallel surfaces can become…

We study rotationally symmetric translators for fully nonlinear extrinsic geometric flows driven by a curvature function, and we establish the fine asymptotics of bowl-type evolutions and, when admissible, the construction and…

If $\xi$ is a Killing vector field of the hyperbolic space $\h^3$ whose flow are parabolic isometries, a surface $\Sigma\subset\h^3$ is a $\xi$-translator if its mean curvature $H$ satisfies $H=\langle N,\xi\rangle$, where $N$ is the unit…

In the half-space model of the hyperbolic three space with the hyperbolic metric, this same space can be seen as the Lie group, hence, a translation surface is a surface that is given by the product of two curves $\alpha$ and $\beta$ in…

We study new examples of translating solitons of the mean curvature flow, especially in Minkowski space. We consider for this purpose manifolds admitting submersions and cohomegeneity one actions by isometries on suitable open subsets. This…

The purpose of these notes is to provide an introduction to those who want to learn more about translating solitons for the mean curvature flow in $\mathbb{R}^3$, particularly those which are complete graphs over domains in $\mathbb{R}^2$.…

We establish the existence of one-parameter families of helicoidal surfaces of $\mathbb H^2\times\mathbb R$ which, under mean curvature flow, simultaneously rotate about a vertical axis and translate vertically.

In this paper, for the Lorentz manifold $M^{2}\times\mathbb{R}$, with $M^{2}$ a $2$-dimensional complete surface with nonnegative Gaussian curvature, we investigate its space-like graphs over compact strictly convex domains in $M^{2}$,…

The translation of an operator is defined by using conjugation with time-frequency shifts. Thus, one can define $\Lambda$-shift-invariant subspaces of Hilbert-Schmidt operators, finitely generated, with respect to a lattice $\Lambda$ in…

In this paper we prove that two-dimensional translating solitons in $\mathbb{R}^3$ with finite $L$-index are homeomorphic to a plane or a cylinder and that a two-dimensional self-expander with finite $L$-index and sub exponential weighted…

In this paper we obtain several properties of translating solitons for a general class of extrinsic geometric curvature flows given by a homogeneous, symmetric, smooth non-negative function $\gamma$ defined in an open cone…

In this paper, we classify the nondegenerate ruled surfaces in the three-dimensional Lorentz-Minkowski space that are homothetic self-similar solutions for the inverse mean curvature flow. This classification shows the existence of two…

In this work we show that $2$-dimensional, simply connected, translating solitons of the mean curvature flow embedded in a slab of $\mathbb{R}^3$ with entropy strictly less than $3$ must be mean convex and thus, thanks to a result by J.…