The uniqueness of the Enneper surfaces and Chern-Ricci functions on minimal surfaces

2017/01/21 by Hojoo Lee, Lee, Hojoo · 1 citation
Mathematics · #49Q05 #53A10 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical analysis #Mathematics #Pure mathematics #Uniqueness #math.DG #msc:49Q05 #msc:53A10

paper · pdf · doi:10.48550/arxiv.1701.05958

published in arXiv (Cornell University) (Cornell University) · Typos corrected, Remark 3.4 revised, Theorem 1.3 restated

openalex publication_date 2017/01/21 · arxiv created 2017/02/01 · arxiv updated 2017/02/02 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We construct the first and second Chern-Ricci functions on negatively curved minimal surfaces in ℝ³ using Gauss curvature and angle functions, and establish that they become harmonic functions on the minimal surfaces. We prove that a minimal surface has constant first Chern-Ricci function if and only if it is Enneper's surface. We explicitly determine the moduli space of minimal surfaces having constant second Chern-Ricci function, which contains catenoids, helicoids, and their associate families.

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