Ruled surfaces of generalized self-similar solutions of the mean\n curvature flow

2020/05/15 by Rafael López, López, Rafael · 1 citation
Mathematics · Physics and Astronomy · #53C42 #53C44 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2005.07660

openalex publication_date 2020/05/15 · openalex created_date 2022/09/16 · openalex updated_date 2026/07/28

Abstract

In Euclidean space, we investigate surfaces whose mean curvature H\nsatisfies the equation H=\α\⟨ N,\x\⟩+\λ, where N\nis the Gauss map, \x is the position vector and \α and\n\λ are two constants. There surfaces generalize self-shrinkers and\nself-expanders of the mean curvature flow. We classify the ruled surfaces and\nthe translation surfaces, proving that they are cylindrical surfaces.\n

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