Two flat structures on minimal surfaces

2018/02/21 by Hojoo Lee, Lee, Hojoo
Mathematics · #49Q05 #53A10 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #math.DG #msc:49Q05 #msc:53A10

paper · pdf · doi:10.48550/arxiv.1802.08169

Comments welcome

arxiv created 2018/02/21 · openalex publication_date 2018/02/21 · arxiv updated 2018/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this expository article, we illustrate how two independent flat structures on minimal surfaces induce a harmonic function, which captures the uniqueness of Enneper's surface.

Related

• Minimal Surface Linear Combinatoin Theorem
• Uniqueness of minimal surfaces, Jacobi fields, and flat structures
• The uniqueness of the Enneper surfaces and Chern-Ricci functions on minimal surfaces
• The number of minimal surfaces bounded by Enneper's wire
• Minimal surfaces over harmonic shears