共查询到20条相似文献,搜索用时 0 毫秒
1.
Rafael López 《Monatshefte für Mathematik》1999,127(2):155-169
We study constant mean curvature compact surfaces immersed in hyperbolic space with non-empty boundary (=H-surfaces). We prove that the only H-surfaces with boundary circular and 0≤∣H∣≤1, are the umbilical examples. When the surface is embedded, conditions to be umbilical are given. Finally, we characterize
umbilical surfaces bounded by a circle among all H-discs with small area.
Received 27 March 1997; in final form 11 June 1998 相似文献
2.
Rafael López 《Annals of Global Analysis and Geometry》2001,20(1):59-75
We study the problem of finding constant mean curvature graphsover a domain of a totally geodesic hyperplane andan equidistant hypersurface Q of hyperbolic space. We findthe existence of graphs of constant mean curvature H overmean convex domains Q and with boundary for –H
< H |h|, where H
> 0 is the mean curvature of the boundary . Here h is the mean curvature respectively of the geodesic hyperplane (h= 0) and of the equidistant hypersurface (0 < |h|< 1). The lower bound on H is optimal. 相似文献
3.
Baris Coskunuzer 《Geometriae Dedicata》2006,118(1):157-171
We study the constant mean curvature (CMC) hypersurfaces in
whose asymptotic boundaries are closed codimension-1 submanifolds in
. We consider CMC hypersurfaces as generalizations of minimal hypersurfaces. We naturally generalize some notions of minimal hypersurfaces like being area-minimizing, convex hull property, exchange roundoff trick to CMC hypersurface context. We also give a generic uniqueness result for CMC hypersurfaces in hyperbolic space. 相似文献
4.
Jorge Herbert S. De Lira 《Geometriae Dedicata》2002,93(1):11-23
The existence is proved of radial graphs with constant mean curvature in the hyperbolic space H
n+1 defined over domains in geodesic spheres of H
n+1 whose boundary has positive mean curvature with respect to the inward orientation. 相似文献
5.
Masatoshi Kokubu 《Geometriae Dedicata》1999,77(3):253-269
We give a representation formula for surfaces of constant mean curvature in Euclidean or hyperbolic space, which is a natural generalization of Weierstrass-Enneper representation formula. The data (two functions) used in our formula should satisfy a certain system of differential equations. The system can be interpreted as an infinite dimensional Hamiltonian system. We investigate two finite-dimensional reductions in detail. 相似文献
6.
Philippe Castillon 《Annals of Global Analysis and Geometry》1999,17(6):563-579
In this work we determine the essential spectrum of the stability operator of a submanifold of the hyperbolic space with constant mean curvature h < 1 and finite total curvature. In some particular cases, we also give a bound on the number of eigenvalues which are below the essential spectrum. 相似文献
7.
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
8.
We use integrable systems techniques to study the singularities of timelike non-minimal constant mean curvature (CMC) surfaces in the Lorentz–Minkowski 3-space. The singularities arise at the boundary of the Birkhoff big cell of the loop group involved. We examine the behavior of the surfaces at the big cell boundary, generalize the definition of CMC surfaces to include those with finite, generic singularities, and show how to construct surfaces with prescribed singularities by solving a singular geometric Cauchy problem. The solution shows that the generic singularities of the generalized surfaces are cuspidal edges, swallowtails, and cuspidal cross caps. 相似文献
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11.
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
12.
本文利用共形度量高斯曲率的估计研究了三维空间形式N^3(C)中具常平均曲率曲面的区域稳定性。 相似文献
13.
本文利用三维欧氏空间R3或三维Minkowski空间R2.1中常平均曲率的曲面与Sinh-Laplace方程和Sinh-Gordon方程之间的关系,研究了常平均曲率的曲面与R2到S2(或H2)及R1.1到S1.1(+1)的调和映照之间的内在联系,并且提供了一种构造到球面S2,H2和S1.1 相似文献
14.
The purpose of this paper is to prove that alocally strongly convex, Euclidean complete surface with constantaffine mean curvature is also affine complete. Consequently weobtain a classification of locally strongly convex, Euclideancomplete surfaces with constant affine mean curvature. 相似文献
15.
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
16.
主要研究了拟常曲率空间中具有常平均曲率的完备超曲面,得到了这类超曲面全脐的一个结果.即若Nn+1的生成元η∈TM,且a-2|b|=c(常数)>0,则当S<2 n-1~(1/2)(a-2|b|)时,M为全脐超曲面. 相似文献
17.
Hypersurfaces with Constant Mean Curvature in Space FormsHypersurfaceswithConstantMeanCurvatureinSpaceForms¥SongHongzao;HuZej... 相似文献
18.
Kilian M.; Kobayashi S.-P.; Rossman W.; Schmitt N. 《Journal London Mathematical Society》2005,72(1):258-272
The paper shows the existence of several new families of noncompactconstant mean curvature surfaces: (i) singly punctured surfacesof arbitrary genus g1, (ii) doubly punctured tori, and (iii)doubly periodic surfaces with Delaunay ends. 相似文献
19.
We investigate the problem of finding, in hyperbolic space, a complete strictly convex hypersurface which has a prescribed
asymptotic boundary at infinity and which has some fixed curvature function being constant. Our results apply to a very general
class of curvature functions. 相似文献
20.
Rafael Lopez 《Geometriae Dedicata》1997,66(3):255-263
This paper proves that an embedded compact surface in the Euclidean space with constant mean curvature H bounded by a circle of radius 1 and included in a slab of width
is a spherical cap. Also, we give partial answers to the problem when a surface with constant mean curvature and planar boundary lies in one of the halfspaces determined by the plane containing the boundary, exactly, when the surface is included in a slab. 相似文献