On complete embedded translating solitons of the mean curvature flow that are of finite genus

Abstract

We desingularise the union of $3$ Grim paraboloids along Costa-Hoffman-Meeks surfaces in order to obtain complete embedded translating solitons of the mean curvature flow with $3$ ends and arbitrary finite genus.

Improved introduction

Cited by in corpus (5)

• Complete translating solitons to the mean curvature flow in ${\mathbb{R}}^3$ with nonnegative mean curvature
• Bi-Halfspace and Convex Hull Theorems for Translating Solitons
• The global geometry of surfaces with prescribed mean curvature in ${\mathbb{R}}^3$
• Translating solitons of the mean curvature flow in the space ${\mathbb{H}}^2\times \mathbb{R}$
• Remarks on topology of stable translating solitons