A CHARACTERIZATION OF THE CATENOID AND HELICOID

DOI10.1142/S0129167X13500456zbMath1270.53006MaRDI QIDQ2842043

Carlos M. C. Riveros, Armando M. V. Corro

Publication date: 30 July 2013

Published in: International Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

minimal surfaceslines of curvatureasymptotic linesChebyshev net

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Meromorphic functions of one complex variable (general theory) (30D30) Representations of solutions to partial differential equations (35C99)

Related Items (3)

Geodesics in minimal surfaces ⋮ Generalized Weingarten surfaces of harmonic type in hyperbolic 3-space ⋮ Unnamed Item

Cites Work

• Un théorème d'unicité de l'hélicoïde. (A uniqueness theorem for the helicoid)
• The geometry of periodic minimal surfaces
• Some uniqueness and nonexistence theorems for embedded minimal surfaces
• Uniqueness and globality of the Liouville formula for entire solutions of \(\frac{\partial^2\log\lambda}{\partial z\partial\overline z} + \frac\lambda2=0\)
• Liouville's formula under the viewpoint of minimal surfaces
• Liouville's formula in arbitrary planar domains
• Bianchi surfaces with constant Chebyshev angle
• Surfaces with constant Chebyshev angle
• Unnamed Item

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