Complete Embedded Self-Translating Surfaces under Mean Curvature Flow

TL;DR

This paper presents a method to construct complete embedded self-translating surfaces under mean curvature flow by desingularizing intersecting grim reapers, advancing understanding of surface evolution in geometric flows.

Contribution

It introduces a novel desingularization technique for intersecting grim reapers to produce new self-translating surfaces under mean curvature flow.

Findings

Successfully constructed new self-translating surfaces

Demonstrated desingularization of intersecting grim reapers

Enhanced understanding of surface behavior in mean curvature flow

Abstract

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.