arXiv research

The paper proves nonexistence results for translating solitons in r-mean curvature flow.

Helicoidal surfaces rotate and translate under mean curvature flow.

The study proves stability of various graphical translators in mean curvature flow.

In this work, we propose a new evolving geometric flow (called translating mean curvature flow) for the translating solitons of hypersurfaces in $R^{n+1}$. We study the basic properties, such as positivity preserving property, of the translating mean curvature flow. The Dirichlet problem for the graphical translating m…

The paper shows translating solitons in $\mathbb{R}^4$ have $SO(2)$ symmetry.

Researchers prove existence and uniqueness of translators for mean curvature flow.

Researchers classify translators and rotators in hyperbolic 3-space for mean curvature flow.

Study classifies translators for mean curvature flow in 3D.

We prove some non-existence theorems for translating solutions to Lagrangian mean curvature flow. More precisely, we show that translating solutions with an $L^2$ bound on the mean curvature are planes and that almost-calibrated translating solutions which are static are also planes. Recent work of D. Joyce, Y.-I. Lee,…

We prove that any complete immersed two-sided mean convex translating soliton $Σ\subset \mathbb{R}^3$ for the mean curvature flow is convex. As a corollary it follows that an entire mean convex graphical translating soliton in $\mathbb{R}^3$ is the axisymmetric "bowl soliton". We also show that if the mean curvature of…

The paper examines translating solitons and their relation to Lagrangian mean curvature flows with zero Maslov class.

This paper classifies complete translating solitons in 3D space.

New proof shows symmetry for certain curved surfaces in higher dimensions.

The paper proves Hessian estimates for specific geometric flows.

Ancient solutions and translators identified for Lagrangian flow.

2-convex translating solitons are locally strictly convex.

The paper classifies surfaces in the Heisenberg space invariant under specific isometries.

Paper proves stability and Dirichlet problem for translating hypersurfaces.

Surveying mean curvature flow on solvmanifolds, focusing on translating solutions.

Study translating solitons in Minkowski space with prescribed Gauss image.

Study classifies minimal surfaces and solitons in hyperbolic 3-space as translation surfaces.

Paper proves translating solutions for a specific flow in a product manifold.

In this paper, we study the convexity, interior gradient estimate, Liouville type theorem and asymptotic behavior at infinity of translating solutions to mean curvature flow as well as the nonlinear flow by powers of the mean curvature.

Proves better rigidity theorems for special solitons.

Study stabilizes translating solitons in hyperbolic space for MCF.

The paper classifies ruled surfaces in a specific space that move in a special way.

Study on rigidity of translating hypersurfaces not in graphical direction.

Study classifies and characterizes translators in hyperbolic static universe.

The paper proves properties of surfaces with finite curvature in 3D space.

The paper proves existence and classification of translating solitons in warped product manifolds.

In the present article we obtain classification results and topological obstructions for the existence of translating solitons of the mean curvature flow.

The paper classifies shapes of translating solitons for a specific flow.

The study finds translators for higher order mean curvature flows in Euclidean and hyperbolic spaces.

The paper classifies special solitons and shrinkers in Euclidean space.

Mean curvature flow converges to a translating soliton with prescribed contact angle.

Researchers create annular translators for mean curvature flow.

The aim of this work is studying translating graphs by mean curvature flow in $\Real^3$. We prove non-existence of complete translating graphs over bounded domains in $\Real^2$. Furthermore, we show that there are only three types of complete translating graphs in $\Real^3$; entire graphs, graphs between two vertical p…

Nguyen's solutions converge to a grim reaper and plane.

We describe a construction of complete embedded self-translating surfaces under mean curvature flow by desingularizing the intersection of a finite family of grim reapers in general position.

The paper proves convexity of certain solitons and expanders in high dimensions.

The paper explores new translating solitons and their relation to $Δ$-wings.

Proves uniqueness of translators in 3D space.

Using certain solutions of the curve shortening flow, including self-shrinking and self-expanding curves or spirals, we construct and characterize many new examples of translating solitons for mean curvature flow in complex Euclidean plane. They generalize the Joyce, Lee and Tsui ones \cite{JLT} in dimension two. The s…

Study shows only grim reaper cylinder for certain self-translating surfaces.

We show that any strictly mean convex translator of dimension $n\geq 3$ which admits a cylindrical estimate and a corresponding gradient estimate is rotationally symmetric. As a consequence, we deduce that any translating solution of the mean curvature flow which arises as a blow-up limit of a two-convex mean curvature…

Study invariant $λ$-translators in Lorentz-Minkowski space.

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 $\mathbb{R}^{3}$ can achieve. On the other hand, we study graphical perturbation…

Paper studies rigidity of translation surfaces in 3D sphere using quaternionic product.