Spectral transformation of constant mean curvature surfaces in H3 and Weierstrass representation

2002 ◽  
Vol 45 (8) ◽  
pp. 1066-1075
Author(s):  
Qing Chen ◽  
Yi Cheng
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Weierstrass Representation ◽  
Constant Mean Curvature Surfaces ◽  
Spectral Transformation

scholarly journals Constant Mean Curvature Surfaces Based on Fundamental Quadrilaterals

2021 ◽  
Vol 24 (4) ◽  
Author(s):  
Alexander I. Bobenko ◽  
Sebastian Heller ◽  
Nick Schmitt
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Weierstrass Representation ◽  
Geometric Flow ◽  
Constant Mean Curvature Surfaces ◽  
Cmc Surfaces

AbstractWe describe the construction of CMC surfaces with symmetries in $\mathbb {S}^{3}$ S 3 and $\mathbb {R}^{3}$ ℝ 3 using a CMC quadrilateral in a fundamental tetrahedron of a tessellation of the space. The fundamental piece is constructed by the generalized Weierstrass representation using a geometric flow on the space of potentials.

scholarly journals Delaunay ends of constant mean curvature surfaces

2008 ◽  
Vol 144 (1) ◽  
pp. 186-220 ◽  
Author(s):  
M. Kilian ◽  
W. Rossman ◽  
N. Schmitt
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Weierstrass Representation ◽  
Curvature Surface ◽  
Regular Singularity ◽  
Constant Mean Curvature Surfaces ◽  
Constant Mean Curvature Surface ◽  
Delaunay Surface

AbstractThe generalized Weierstrass representation is used to analyze the asymptotic behavior of a constant mean curvature surface that arises locally from an ordinary differential equation (ODE) with a regular singularity. We prove that a holomorphic perturbation of an ODE that represents a Delaunay surface generates a constant mean curvature surface which has a properly immersed end that is asymptotically Delaunay. Furthermore, that end is embedded if the Delaunay surface is unduloidal.

scholarly journals Biharmonic constant mean curvature surfaces in Killing submersions

2018 ◽  
Vol 133 ◽  
pp. 91-101
Author(s):  
Stefano Montaldo ◽  
Irene I. Onnis ◽  
Apoena Passos Passamani
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Constant Mean Curvature Surfaces
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