Dynamical stability of various convex graphical translators
Junyoung Park
TL;DR
This paper proves the existence of long-term solutions to mean curvature flow from certain graphs and establishes the dynamical stability of various graphical translators, including grim reaper and cylindrical types.
Contribution
It introduces new stability results for multiple types of graphical translators in mean curvature flow, extending understanding of their long-term behavior.
Findings
Existence of long-time solutions from graphs over slabs.
Dynamical stability of grim reaper and other translators.
Stability results for asymptotically cylindrical translators.
Abstract
In the first part of the paper, we prove the existence of longtime solution to mean curvature flow starting from a graph of a continuous function defined over a slab. Then, we establish dynamical stability results for various types of graphical translators to mean curvature flow, namely the grim reaper, two dimensional graphical translators, and asymptotically cylindrical translators.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Numerical methods in inverse problems