Complete surfaces inE 3 with constant mean curvature

1966 ◽  
Vol 41 (1) ◽  
pp. 313-318 ◽  
Author(s):  
Tilla Klotz ◽  
Robert Osserman
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Complete Surfaces

On the Gauss map of complete surfaces of constant mean curvature in R3 and R4

1982 ◽  
Vol 57 (1) ◽  
pp. 519-531 ◽  
Author(s):  
D. A. Hoffman ◽  
R. Osserman ◽  
R. Schoen
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Gauss Map ◽  
Complete Surfaces

Complete Surfaces of Constant Mean Curvature-1 in the Hyperbolic 3-space

1993 ◽  
Vol 137 (3) ◽  
pp. 611 ◽  
Author(s):  
Masaaki Umehara ◽  
Kotaro Yamada
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Complete Surfaces

scholarly journals PARABOLIC AND HYPERBOLIC SCREW MOTION SURFACES IN ℍ2×ℝ

2008 ◽  
Vol 85 (1) ◽  
pp. 113-143 ◽  
Author(s):  
RICARDO SA EARP
Keyword(s):  
Minimal Surface ◽  
Explicit Formula ◽  
Mean Curvature ◽  
Product Space ◽  
Constant Mean Curvature ◽  
Screw Motion ◽  
Entire Vertical Graphs ◽  
Screw Motions ◽  
Simply Connected ◽  
Complete Surfaces

AbstractIn this paper we find many families in the product space ℍ2×ℝ of complete embedded, simply connected, minimal and surfaces with constant mean curvature H such that |H|≤1/2. We study complete surfaces invariant either by parabolic or by hyperbolic screw motions. We study the notion of isometric associate immersions. We exhibit an explicit formula for a Scherk-type minimal surface. We give a one-parameter family of entire vertical graphs of mean curvature 1/2. We prove a generalized Bour lemma that can be applied to ℍ2×ℝ,𝕊2×ℝ and to Heisenberg’s space to produce a family of screw motion surfaces isometric to a given one.

scholarly journals COMPLETE SURFACES IN $E^3$ WITH CONSTANT MEAN CURVATURE

1991 ◽  
Vol 22 (1) ◽  
pp. 79-82
Author(s):  
MEHMET ERDOGAN ◽  
TAKEHIRO ITOH
Keyword(s):  
Gaussian Curvature ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Complete Surfaces

We give a classification of surfaces in $E^3$ with constant mean curvature and the Gaussian curvature $K$ not changing its sign around some point at which $K$ vanishes.

scholarly journals On far-outlying constant mean curvature spheres in asymptotically flat Riemannian 3-manifolds

2020 ◽  
Vol 2020 (767) ◽  
pp. 161-191
Author(s):  
Otis Chodosh ◽  
Michael Eichmair
Keyword(s):  
Scalar Curvature ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Existence Results ◽  
Asymptotically Flat ◽  
Weingarten Surfaces ◽  
Differential Geom

AbstractWe extend the Lyapunov–Schmidt analysis of outlying stable constant mean curvature spheres in the work of S. Brendle and the second-named author [S. Brendle and M. Eichmair, Isoperimetric and Weingarten surfaces in the Schwarzschild manifold, J. Differential Geom. 94 2013, 3, 387–407] to the “far-off-center” regime and to include general Schwarzschild asymptotics. We obtain sharp existence and non-existence results for large stable constant mean curvature spheres that depend delicately on the behavior of scalar curvature at infinity.

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