The sharp isoperimetric inequality for minimal surfaces with radially connected boundary in hyperbolic space

1992 ◽  
Vol 109 (1) ◽  
pp. 495-503 ◽  
Author(s):  
Jaigyoung Choe ◽  
Robert Gulliver
Keyword(s):  
Isoperimetric Inequality ◽  
Hyperbolic Space ◽  
Minimal Surfaces

Stability of minimal surfaces in a 3-dimensional hyperbolic space

1981 ◽  
Vol 36 (1) ◽  
pp. 554-557 ◽  
Author(s):  
J. L. Barbosa ◽  
M. do Carmo
Keyword(s):  
Hyperbolic Space ◽  
Minimal Surfaces ◽  
3 Dimensional

New minimal surfaces in the hyperbolic space

2017 ◽  
Vol 60 (9) ◽  
pp. 1679-1704
Author(s):  
NingWei Cui ◽  
Keti Tenenblat
Keyword(s):  
Hyperbolic Space ◽  
Minimal Surfaces

The isoperimetric inequality for minimal surfaces in a Riemannian manifold

1999 ◽  
Vol 1999 (506) ◽  
pp. 205-214 ◽  
Author(s):  
Jaigyoung Choe
Keyword(s):  
Riemannian Manifold ◽  
Minimal Surface ◽  
Sectional Curvature ◽  
Isoperimetric Inequality ◽  
Gaussian Curvature ◽  
Minimal Surfaces ◽  
Constant Gaussian Curvature ◽  
Simply Connected

Abstract It is proved that every minimal surface with one or two boundary components in a simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant K satisfies the sharp isoperimetric inequality 4π A ≦ L2 + K A2. Here equality holds if and only if the minimal surface is a geodesic disk in a surface of constant Gaussian curvature K.

scholarly journals Minimal surfaces in euclidean 3-space and their mean curvature 1 cousins in hyperbolic 3-space

2003 ◽  
Vol 75 (3) ◽  
pp. 271-278
Author(s):  
Shoichi Fujimori
Keyword(s):  
Minimal Surface ◽  
Hyperbolic Space ◽  
Minimal Surfaces ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
3 Dimensional

We show that the Hopf differentials of a pair of isometric cousin surfaces, a minimal surface in euclidean 3-space and a constant mean curvature (CMC) one surface in the 3-dimensional hyperbolic space, with properly embedded annular ends, extend holomorphically to each end. Using this result, we derive conditions for when the pair must be a plane and a horosphere.

scholarly journals Helicoidal minimal surfaces in hyperbolic space

1989 ◽  
Vol 114 ◽  
pp. 65-75 ◽  
Author(s):  
Jaime B. Ripoll
Keyword(s):  
Hyperbolic Space ◽  
Minimal Surfaces ◽  
3 Dimensional ◽  
Helicoidal Surfaces ◽  
Helicoidal Surface ◽  
Sectional Curvatures ◽  
The One ◽  
Group Of Isometries

Denote by H3 the 3-dimensional hyperbolic space with sectional curvatures equal to – 1, and let g be a geodesic in H3 Let {ψt} be the translation along g (see § 2) and let {φt} be the one-parameter subgroup of isometries of H3 whose orbits are circles centered on g. Given any α ∊ R, one can show that λ = {λt} = ψt ∘ φαt} is a one-parameter subgroup of isometries of H3 (see § 2) which is called a helicoidal group of isometries with angular pitch α. Any surface in H3 which is λ-invariant is called a helicoidal surface.In this work we prove some results concerning minimal helicoidal surfaces in H3. The first one reads:

scholarly journals Integrability properties of minimal surfaces in hyperbolic space

2018 ◽  
Vol 965 ◽  
pp. 012017
Author(s):  
Yifei He ◽  
Changyu Huang ◽  
Martin Kruczenski
Keyword(s):  
Hyperbolic Space ◽  
Minimal Surfaces
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