共查询到20条相似文献,搜索用时 46 毫秒
1.
《Journal de Mathématiques Pures et Appliquées》1999,78(7):667-700
In this paper, we give general curvature estimates for constant mean curvature surfaces immersed into a simply-connected 3-dimensional space form. We obtain bounds on the norm of the traceless second fundamental form and on the Gaussian curvature at the center of a relatively compact stable geodesic ball (and, more generally, of a relatively compact geodesic ball with stability operator bounded from below). As a by-product, we show that the notions of weak and strong Morse indices coincide for complete non-compact constant mean curvature surfaces. We also derive a geometric proof of the fact that a complete stable surface with constant mean curvature 1 in the usual hyperbolic space must be a horosphere. 相似文献
2.
Wayne Rossman 《Journal of Geometric Analysis》2001,11(4):669-692
We describe local similarities and global differences between minimal surfaces in Euclidean 3-space and constant mean curvature
1 surfaces in hyperbolic 3-space. We also describe how to solve global period problems for constant mean curvature 1 surfaces
in hyperbolic 3-space, and we give an overview of recent results on these surfaces. We include computer graphics of a number
of examples. 相似文献
3.
By using the method of integrable system, we study the deformation of constant mean curvature surfaces in three-dimensional hyperbolic space form H3. We also obtain a Weierstrass representation formula of the constant mean curvature surfaces with mean curvature greater than 1. 相似文献
4.
By using the method of integrable system, we study the deformation of constant mean curvature surfaces in three-dimensional hyperbolic space form H3. We also obtain a Weierstrass representation formula of the constant mean curvature surfaces with mean curvature greater than 1 相似文献
5.
By using the method of integrable system, we study the deformation of constant mean curvature surfaces in three-dimensional
hyperbolic space form H3. We also obtain a Weierstrass representation formula of the constant mean curvature surfaces with mean curvature greater
than 1 相似文献
6.
Christian Müller 《Discrete and Computational Geometry》2014,51(3):516-538
Recently, a curvature theory for polyhedral surfaces has been established that associates with each face a mean curvature value computed from areas and mixed areas of that face and its corresponding Gaussian image face. Therefore, a study of constant mean curvature (cmc) surfaces requires studying pairs of polygons with some constant nonvanishing value of the discrete mean curvature for all faces. We focus on meshes where all faces are planar quadrilaterals or planar hexagons. We show an incidence geometric characterization of a pair of parallel quadrilaterals having a discrete mean curvature value of ?1. This characterization yields an integrability condition for a mesh being a Gaussian image mesh of a discrete cmc surface. Thus, we can use these geometric results for the construction of discrete cmc surfaces. In the special case where all faces have a circumcircle, we establish a discrete Weierstrass-type representation for discrete cmc surfaces. 相似文献
7.
Atsushi Fujioka 《Proceedings of the American Mathematical Society》1999,127(10):3021-3025
We define surfaces with harmonic inverse mean curvature in space forms and generalize a theorem due to Lawson by which surfaces of constant mean curvature in one space form isometrically correspond to those in another. We also obtain an immersion formula, which gives a deformation family for these surfaces.
8.
T. Sasahara 《Acta Mathematica Hungarica》2014,144(2):433-448
We completely classify λ-biharmonic slant surfaces and λ-biminimal Lagrangian surfaces in 2-dimensional complex space forms, under the condition that the mean curvature is nonzero constant. In addition, we provide some examples of λ-biminimal slant surfaces with nonzero constant mean curvature, which are neither Lagrangian nor λ-biharmonic. 相似文献
9.
Ronaldo F. de Lima 《Annals of Global Analysis and Geometry》2001,20(4):325-343
Maximum principles at infinity generalize Hopf's maximum principle for hypersurfaces with constant mean curvature in R
n
. We establish such a maximum principle for parabolic surfaces in R3 with nonzero constant mean curvature and bounded Gaussian curvature. 相似文献
10.
Shinya Hirakawa 《Geometriae Dedicata》2006,118(1):229-244
We classify constant Gaussian curvature surfaces with nonzero parallel mean curvature vector in two-dimensional complex space forms. As a result, we find new examples of such surfaces. 相似文献
11.
Rafael López 《Geometriae Dedicata》1999,76(1):81-95
We prove that a spacelike surface in L3 with nonzero constant mean curvature and foliated by pieces of circles in spacelike planes is a surface of revolution. When the planes containing the circles are timelike or null, examples of nonrotational constant mean curvature surfaces constructed by circles are presented. Finally, we prove that a nonzero constant mean curvature spacelike surface foliated by pieces of circles in parallel planes is a surface of revolution. 相似文献
12.
Miyuki Koiso Bennett Palmer 《Calculus of Variations and Partial Differential Equations》2012,43(3-4):555-587
We study the stability of surfaces trapped between two parallel planes with free boundary on these planes. The energy functional consists of anisotropic surface energy, wetting energy, and line tension. Equilibrium surfaces are surfaces with constant anisotropic mean curvature. We study the case where the Wulff shape is of “product form”, that is, its horizontal sections are all homothetic and have a certain symmetry. Such an anisotropic surface energy is a natural generalization of the area of the surface. In particular, we study the stability of parts of anisotropic Delaunay surfaces which arise as equilibrium surfaces. They are surfaces of the same product form of the Wulff shape. We show that, for these surfaces, the stability analysis can be reduced to the case where the surface is axially symmetric and the functional is replaced by an appropriate axially symmetric one. Moreover, we obtain necessary and sufficient conditions for the stability of anisotropic sessile drops. 相似文献
13.
Hoeskuldur P. Halldorsson 《Geometriae Dedicata》2013,162(1):45-65
We describe all possible self-similar motions of immersed hypersurfaces in Euclidean space under the mean curvature flow and derive the corresponding hypersurface equations. Then we present a new two-parameter family of immersed helicoidal surfaces that rotate/translate with constant velocity under the flow. We look at their limiting behaviour as the pitch of the helicoidal motion goes to 0 and compare it with the limiting behaviour of the classical helicoidal minimal surfaces. Finally, we give a classification of the immersed cylinders in the family of constant mean curvature helicoidal surfaces. 相似文献
14.
In this note we study constant mean curvature surfaces in asymptotically flat 3-manifolds. We prove that, outside a given compact subset in an asymptotically flat 3-manifold with positive mass, stable spheres of given constant mean curvature are unique. Therefore we are able to conclude that the foliation of stable spheres of constant mean curvature in an asymptotically flat 3-manifold with positive mass outside a given compact subset is unique.
15.
We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean
and Gaussian curvatures of faces are derived from the faces’ areas and mixed areas. Remarkably these notions are capable of
unifying notable previously defined classes of surfaces, such as discrete isothermic minimal surfaces and surfaces of constant
mean curvature. We discuss various types of natural Gauss images, the existence of principal curvatures, constant curvature
surfaces, Christoffel duality, Koenigs nets, contact element nets, s-isothermic nets, and interesting special cases such as
discrete Delaunay surfaces derived from elliptic billiards. 相似文献
16.
In this work we extend the Weierstrass representation for maximal spacelike surfaces in the 3-dimensional Lorentz-Minkowski space to spacelike surfaces whose mean curvature is proportional to its Gaussian curvature (linear Weingarten surfaces of maximal type). We use this representation in order to study the Gaussian curvature and the Gauss map of such surfaces when the immersion is complete, proving that the surface is a plane or the supremum of its Gaussian curvature is a negative constant and its Gauss map is a diffeomorphism onto the hyperbolic plane. Finally, we classify the rotation linear Weingarten surfaces of maximal type. 相似文献
17.
We extend an original idea of Calabi for affine maximal surfaces and define
a sextic holomorphic differential form for affine surfaces with constant affine mean
curvature. We get some rigidity results for affine complete surfaces by using this
sextic holomorphic form.
Received: 17 May 2003 相似文献
18.
Using a Weierstrass type representation of constant mean curvature surfaces, we give a general method for constructing constant
mean curvature n-noids (of genus 0) from holomorphic potentials, where n ≥ 3. The ends of these surfaces are embedded and asymptotically approach Delaunay surfaces, while the surfaces are in general
not even almost embedded. In particular, a 3-parameter family of constant mean curvature trinoids is constructed.
Part of this work was done, while the first named author held a Lehrstuhlvertretung at the University of Augsburg. He would
like to thank the University of Augsburg for its hospitality. He would also like to acknowledge partial support by DFG-grant
DO 776. 相似文献
19.
Young Wook Kim Sung-Eun Koh Heayong Shin Seong-Deog Yang 《manuscripta mathematica》2007,124(3):343-361
Surfaces in Euclidean three-space with constant ratio of mean curvature to Gauss curvature arise naturally as the parallel surfaces to minimal surfaces. They might possess singularities which occur naturally as focal points of minimal surfaces. We study geometric properties and the singularities of such surfaces, prove some global results about them, and provide a Björling formula to construct such surfaces with prescribed point or curve singularities. 相似文献
20.
Huai-Dong Cao Ying Shen Shunhui Zhu 《Calculus of Variations and Partial Differential Equations》1998,7(2):141-157
We obtain a gradient estimate for the Gauss maps from complete spacelike constant mean curvature hypersurfaces in Minkowski
space into the hyperbolic space. As an application, we prove a Bernstein theorem which says that if the image of the Gauss
map is bounded from one side, then the spacelike constant mean curvature hypersurface must be linear. This result extends
the previous theorems obtained by B. Palmer [Pa] and Y.L. Xin [Xin1] where they assume that the image of the Gauss map is
bounded. We also prove a Bernstein theorem for spacelike complete surfaces with parallel mean curvature vector in four-dimensional
spaces.
Received July 4, 1997 / Accepted October 9, 1997 相似文献