# Graphical translators for anisotropic and crystalline mean curvature flow

@inproceedings{Cesaroni2021GraphicalTF, title={Graphical translators for anisotropic and crystalline mean curvature flow}, author={Annalisa Cesaroni and Heiko Kroener and Matteo Novaga}, year={2021} }

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 anisotropy and the mobility. In these cases, the equation becomes an ordinary differential equation, and this allows to find explicitly the translators and describe their main features.

#### References

SHOWING 1-10 OF 34 REFERENCES

Existence and uniqueness for a crystalline mean curvature flow

- Mathematics
- 2015

An existence and uniqueness result, up to fattening, for a class of crystalline mean curvature flows with natural mobility is proved. The results are valid in any dimension and for arbitrary,… Expand

A level set crystalline mean curvature flow of surfaces

- Mathematics, Physics
- 2016

We introduce a new notion of viscosity solutions for the level set formulation of the motion by crystalline mean curvature in three dimensions. The solutions satisfy the comparison principle,… Expand

Existence and uniqueness for anisotropic and crystalline mean curvature flows

- Mathematics
- Journal of the American Mathematical Society
- 2019

An existence and uniqueness result, up to fattening, for crystalline mean curvature flows with forcing and arbitrary (convex) mobilities, is proven. This is achieved by introducing a new notion of… Expand

Anisotropic motion by mean curvature in the context of Finsler geometry

- Mathematics
- 1996

Abstract. We study the anisotropic motion of a hypersurface in the context of the geometry of Finsler spaces. This amounts in considering the evolution in relative geometry, where all quantities are… Expand

Complete translating solitons to the mean curvature flow in ℝ3 with nonnegative mean curvature

- Mathematics
- 2020

We prove that any complete immersed two-sided mean convex translating soliton Σ ⊂ R for the mean curvature flow is convex. As a corollary it follows that an entire mean convex graphical translating… Expand

Anisotropic mean curvature flow of Lipschitz graphs and convergence to self-similar solutions

- Mathematics
- ESAIM: Control, Optimisation and Calculus of Variations
- 2021

We consider the anisotropic mean curvature flow of entire Lipschitz graphs. We prove existence and uniqueness of expanding self-similar solutions which are asymptotic to a prescribed cone, and we… Expand

Crystalline Mean Curvature Flow of Convex Sets

- Mathematics
- 2006

We prove a local existence and uniqueness result of crystalline mean curvature flow starting from a compact convex admissible set in . This theorem can handle the facet breaking/bending phenomena,… Expand

Generalized crystalline evolutions as limits of flows with smooth anisotropies

- Mathematics
- Analysis & PDE
- 2019

We prove existence and uniqueness of weak solutions to anisotropic and crystalline mean curvature flows, obtained as limit of the viscosity solutions to flows with smooth anisotropies.

Stability of translating solutions to mean curvature flow

- Mathematics
- 2005

We prove stability of rotationally symmetric translating solutions to mean curvature flow. For initial data that converge spatially at infinity to such a soliton, we obtain convergence for large… Expand

Regularity Theory for Mean Curvature Flow

- Mathematics
- 2003

1 Introduction.- 2 Special Solutions and Global Behaviour.- 3 Local Estimates via the Maximum Principle.- 4 Integral Estimates and Monotonicity Formulas.- 5 Regularity Theory at the First Singular… Expand