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Translators of the mean curvature flow in the special linear group SL(2,ℝ)

2024/05/24 by Rafael López, Marian Ioan Munteanu, López, Rafael +1
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2405.15957

openalex publication_date 2024/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Translators in the special linear group SL(2,ℝ) are surfaces whose mean curvature H and unit normal vector N satisfy H=⟨ N,X⟩, where X is a fixed Killing vector field. In this paper we study and classify those translators that are invariant by a one-parameter group of isometries. By the Iwasawa decomposition, there are three types of such groups. The dimension of the Killing vector fields is 4 and an exhaustive discussion is done for each one of the Killing vector fields and each of the invariant surfaces. In some cases, explicit parametrizations of translators are obtained.

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