相关论文: Translating solitons for Lagrangian mean curvature…
We construct new examples of self-similar solutions and translating solitons for Lagrangian mean curvature flow by extending the method of Joyce, Lee and Tsui. Those examples include examples in which the Lagrangian angle is arbitrarily…
We construct many self-similar and translating solitons for Lagrangian mean curvature flow, including self-expanders and translating solitons with arbitrarily small oscillation on the Lagrangian angle. Our translating solitons play the same…
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…
In this paper, we consider $\lambda$-translating solitons and $\lambda$-shrinkers of the Gauss curvature flow in Euclidean space. We prove that planes and circular cylinders are the only $\lambda$-translating solitons with constant mean…
We classify all Hamiltonian stationary Lagrangian surfaces in complex Euclidean plane which are self-similar solutions of the mean curvature flow.
We obtain explicit solutions of the mean curvature flow in some submanifolds of the Euclidean space. We give particularly an explicit solution of the flow of a hypersurface in the Lagrangian self-expander $L$ which is constructed in the…
We introduce a new method to construct a large family of Lagrangian surfaces in complex Euclidean plane by means of two planar curves making use of their usual product as complex functions and integrating the Hermitian product of their…
In this paper, we construct various examples of Lagrangian mean curvature flows in Calabi-Yau manifolds, using moment maps for actions of abelian Lie groups on them. The examples include Lagrangian self-shrinkers and translating solitons in…
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…
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…
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 $\mathbb{R}^2$.…
In this paper we study the theory of self translating solitons of the mean curvature flow of immersed surfaces in the product space $\mathbb{H}^2\times\mathbb{R}$. We relate this theory to the one of manifolds with density, and exploit this…
It is known that there is no a Type I singularity for the Lagrangian mean curvature flow with zero Maslov class. In this paper, we study translating solitons which are important models of Type II singularities. A necessary condition for a…
We construct Lagrangian translating solitons by desingularizing the intersection points between Lagrangian Grim Reaper cylinders with the same phase using special Lagrangian Lawlor necks. The resulting Lagrangian translating solitons could…
In the present article we obtain classification results and topological obstructions for the existence of translating solitons of the mean curvature flow.
A translating soliton is a hypersurface $M$ in $\mathbb{R}^{n+1}$ such that the family $M_t= M- t \,\mathbf{e}_{n+1}$ is a mean curvature flow, i.e., such that normal component of the velocity at each point is equal to the mean curvature at…
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…
Motivated by Ilmanen's correspondence, we present an explicit solution to the prescribed Hoffman-Osserman Gauss map problem for non-minimal translators to the mean curvature flow in Euclidean 4-space. We propose a conjecture on the…
We study solutions to the inverse mean curvature flow which evolve by homotheties of a given submanifold with arbitrary dimension and codimension. We first show that the closed ones are necessarily spherical minimal immersions and so we…
Suppose that $\mathcal{M}$ is an almost calibrated, exact, ancient solution of Lagrangian mean curvature flow in $\mathbb{C}^n$. We show that if $\mathcal{M}$ has a blow-down given by the static union of two Lagrangian subspaces with…