Higher genus Angel surfaces

2025/09/04 by Bardhan, Rivu, Biswas, Indranil, Fujimori, Shoichi +1
#30F60 #49Q05 #53A10 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.03925

Abstract

We prove the existence of complete minimal surfaces in ℝ³ of arbitrary genus p ≥ 1 and least total absolute curvature with precisely two ends -- one catenoidal and one Enneper-type -- thereby solving, affirmatively, a problem posed by Fujimori and Shoda. These surfaces, which are called Angel surfaces, generalize some examples numerically constructed earlier by Weber. The construction of these minimal surfaces involves extending the orthodisk method developed by Weber and Wolf \citeweber2002teichmuller. A central idea in our construction is the notion of partial symmetry, which enables us to introduce controlled symmetry into the surface.

Citations

• Higher genus maxfaces with Enneper end
• Minimal Surfaces of Least Total Curvature and Moduli Spaces of Plane Polygonal Arcs

Related

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• An example of a minimal surface of genus one with two catenoid ends and one Enneper end
• Minimal Surfaces of Least Total Curvature and Moduli Spaces of Plane Polygonal Arcs
• Higher genus Riemann minimal surfaces
• Minimal Surfaces of Finite Genus: Classification, Dynamics and Laminations