Year: 2025
Type: preprint
Abstract: We prove the existence of complete minimal surfaces in $\mathbb{R}^3$ of arbitrary genus $p\, \ge\, 1$ 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 \emph{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 \cite{weber2002teichmuller}. A central idea in our construction is the notion of \emph{partial symmetry}, which enables us to introduce controlled symmetry into the surface.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7080136200
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