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 Constant mean curvature surfaces with circular boundary in R³

2006 ◽  
Vol 78 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Pedro A. Hinojosa
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Spherical Cap ◽  
Constant Mean Curvature Surfaces ◽  
Circular Boundary ◽  
Cmc Surfaces ◽  
Global Estimates ◽  
Area And Volume

In this work we deal with surfaces immersed in R³ with constant mean curvature and circular boundary. We improve some global estimates for area and volume of such immersions obtained by other authors. We still establish the uniqueness of the spherical cap in some classes of cmc surfaces.

scholarly journals Singularities of spacelike constant mean curvature surfaces in Lorentz–Minkowski space

2011 ◽  
Vol 150 (3) ◽  
pp. 527-556 ◽  
Author(s):  
DAVID BRANDER
Keyword(s):  
Vector Field ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Singular Set ◽  
Constant Mean Curvature Surfaces ◽  
Cmc Surfaces ◽  
Real Analytic ◽  
Cuspidal Edge ◽  
Zero Mean Curvature ◽  
Tangent Field

AbstractWe study singularities of spacelike, constant (non-zero) mean curvature (CMC) surfaces in the Lorentz–Minkowski 3-space L3. We show how to solve the singular Björling problem for such surfaces, which is stated as follows: given a real analytic null-curve f0(x), and a real analytic null vector field v(x) parallel to the tangent field of f0, find a conformally parameterized (generalized) CMC H surface in L3 which contains this curve as a singular set and such that the partial derivatives fx and fy are given by df0/dx and v along the curve. Within the class of generalized surfaces considered, the solution is unique and we give a formula for the generalized Weierstrass data for this surface. This gives a framework for studying the singularities of non-maximal CMC surfaces in L3. We use this to find the Björling data – and holomorphic potentials – which characterize cuspidal edge, swallowtail and cuspidal cross cap singularities.

scholarly journals Notes on constant mean curvature surfaces and their graphical presentation

Filomat ◽  
2009 ◽  
Vol 23 (2) ◽  
pp. 97-107 ◽  
Author(s):  
Marija Ciric
Keyword(s):  
Computer Program ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Constant Mean Curvature Surfaces ◽  
Cmc Surfaces ◽  
Graphical Presentation

In this paper graphical presentation some of the constant mean curvature surfaces (CMC surfaces) is given. This work is an extension of the results [3]. Interesting shapes and complicate structures of CMC surfaces obtained using Mathematica computer program are given.

Sign in / Sign up

Export Citation Format

Share Document