arXiv research

Constructing translating solitons from Lagrangian Grim Reapers.

Symplectic solitons rigid if bounded, study shows.

Improved understanding of translating solitons using new techniques.

In this paper, we compute the first and second variation formulas for the F-functional of translating solitons and study the Hamiltonian L-stability of Lagrangian translating solitons. We prove that any Lagrangian translating soliton is Hamiltonian L-stable.

Characterizes ruled translating solitons in Minkowski 3-space.

Study proves conditions for translating solitons to be planar.

Classifies timelike translating solitons in Minkowski space.

Proves better rigidity theorems for special solitons.

Paper proves stability and Dirichlet problem for translating hypersurfaces.

In this paper, we investigate the parametric version and non-parametric version of rigidity theorem of spacelike translating solitons in pseudo-Euclidean space $\mathbb{R}^{m+n}_{n}$. Firstly, we classify $m$-dimensional complete spacelike translating solitons in $\mathbb{R}^{m+n}_{n}$ by affine technique and classical…

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

The study finds complete translating solitons for certain powers of Gaussian curvature in Riemannian products.

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

Study stabilizes translating solitons in hyperbolic space for MCF.

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

We show that any complete $f$-stable translating soliton $M$ admits no codimension one cycle which does not disconnect $M$. As a corollary, it follows that any two dimensional complete $f$-stable translating soliton has genus zero.

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…

New curves defined by curvature powers studied for variational properties.

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

Paper provides a formula for translating solitons and singular minimal surfaces.

In this paper, we study entire spacelike translating solitons in Minkowski space. By constructing convex spacelike solutions to (1.3) in bounded convex domains, we obtain many entire smooth convex strictly spacelike translating solitons by prescribing boundary data at infinity.

In this paper, we prove a monotonicity formula and some Bernstein type results for translating solitons of hypersurfaces in $\re^{n+1}$, giving some conditions under which a trantranslating soliton is a hyperplane. We also show a gap theorem for the translating soliton of hypersurfaces in $R^{n+k}$, namely, if the $L^n…

The paper studies minimal surface flow and translating solitons, proving global solutions and convergence.

Paper finds convexity in translating solitons for concave flows.

We prove that any complete immersed globally orientable uniformly 2-convex translating soliton $Σ\subset \mathbb{R}^{n+1}$ for the mean curvature flow is locally strictly convex. It follows that a uniformly 2-convex entire graphical translating soliton in $\mathbb{R}^{n+1},\, n\geq 3$ is the axisymmetric "bowl soliton…

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

The study classifies translating and self-expanding solitons in 3D space.

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

The paper classifies special solitons and shrinkers in Euclidean space.

We study volume growth, entropy and stability for translating solitons of mean curvature flow. First, we prove that every complete properly immersed translator has at least linear volume growth. Then, by using Huisken's monotonicity formula, we compute the entropy of the grim reaper and the bowl solitons. We also give …

In this paper, we prove that any Lagrangian translating soliton is Lagrangian $L$-stable.

The paper proves rigidity and vanishing theorems for translating solitons.

Study classifies translating solitons in Minkowski 3-space, revealing singularities.

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

Study expanding gradient Ricci solitons with Euclidean base.

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

Finite entropy translating solitons in slabs have quantized entropy and unique structure.

Classifies and constructs translators for curvature flows.

The paper proves instability of translating λ-solitons and provides bounds on their length.

Study translating solitons in Minkowski space with prescribed Gauss image.

We study some basic problems of translating solitons: the volume growth, generalized maximum principle, Gauss maps and certain functions related to the Gauss maps, finally we carry out point-wise estimates and integral estimates for the squared norm of the second fundamental form. Those estimates give rigidity theorems…

In this paper, we construct finite blow-up examples for symplectic mean curvature flows and we study properties of symplectic translating solitons. We prove that, the Kähler angle $α$ of a symplectic translating soliton with $\max |A|=1$ satisfies that $\sup |α|>\fracπ{4}\frac{|T|}{|T|+1}$ where $T$ is the direction in…

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

In this paper, we study the properties of potential function of the translating soliton $M$ in $R^{n+1}$ and the volume growth of the intersection of Euclidean balls with $M$. We give a condition to obtain the Bernstein theorem for the translating solitons. We also give an outline of a simple proof of the Bernstein the…

The paper classifies invariant gradient $k$-Yamabe solitons in pseudo-Euclidean spaces.

We give an analytic approach to the translating soliton equation with a special emphasis in the study of the Dirichlet problem in convex domains of the plane.

The paper extends convexity results for translating solitons in higher dimensions.

New families of translating solitons found in hyperbolic space.