Minimal surfaces in Euclidean space with a log-linear density

2014/10/09 by Rafael López, López, Rafael
Computer Science · Mathematics · #53A10 #53C44 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1410.2517

openalex publication_date 2014/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study surfaces in Euclidean space \mathbb R³ that are minimal for a log-linear density ϕ(x,y,z)=αx+βy+γy, where α,β,γ are real numbers not all zero. We prove that if a surface is ϕ-minimal foliated by circles in parallel planes, then these planes are orthogonal to the vector (α,β,γ) and the surface must be rotational. We also classify all minimal surfaces of translation type.

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