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

2017/01/21 by Lee, Hojoo
#49Q05 #53A10 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1701.05958

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.

Related

• Two flat structures on minimal surfaces
• Minimal surfaces that attain equality in the Chern-Osserman inequality
• An example of a minimal surface of genus one with two catenoid ends and one Enneper end
• On Chern minimal surfaces in Hermitian surfaces
• The number of minimal surfaces bounded by Enneper's wire