Singular minimal surfaces with constant curvature
Rafael L\'opez
TL;DR
This paper classifies singular minimal surfaces with constant curvature, showing they are limited to planes, spheres, and cylinders, and further classifies those with constant principal or mean curvature.
Contribution
It provides a comprehensive classification of singular minimal surfaces with constant curvature properties, expanding understanding of their geometric structure.
Findings
Singular minimal surfaces with constant Gauss curvature are planes, spheres, or cylinders.
Classified all singular minimal surfaces with constant principal curvature.
Classified all singular minimal surfaces with constant mean curvature.
Abstract
We prove that singular minimal surfaces with constant Gauss curvature are planes, spheres and cylindrical surfaces. We also classify all singular minimal surfaces with a constant principal curvature and singular minimal surfaces with constant mean curvature.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Advanced Differential Geometry Research