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

Graham Smith

Vol. 17 (2024), No. 4, 1175–1236
Abstract

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

Keywords
mean curvature flow, soliton, singular perturbation, Costa–Hoffman–Meeks surface, Grim paraboloid, bowl soliton
Mathematical Subject Classification 2010
Primary: 53C44
Milestones
Received: 17 December 2019
Revised: 13 August 2022
Accepted: 23 September 2022
Published: 17 May 2024
Authors
Graham Smith
Departamento de Matemática
Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio)
Rio de Janeiro
Brazil

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