A Weierstrass type representation for translating solitons and singular minimal surfaces

2022/01/04 by Antonio Martínez, Martínez, Antonio, A. L. Martínez-Triviño +1 · 2 citations
Mathematics · Physics and Astronomy · #35J60 #53C42 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2201.01192

openalex publication_date 2022/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we provide a Weierstrass representation formula for translating solitons and singular minimal surfaces in ℝ³. As application we study when the euclidean Gauss map has a harmonic argument and solve a general Cauchy problem in this class of surfaces.

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• On the first Neumann eigenvalue for critical points of a weighted area functional with asymptotically flat ends
• Minimal (n-2)-umbilic submanifolds of the Euclidean space

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