共查询到20条相似文献,搜索用时 8 毫秒
1.
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
2.
3.
4.
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
5.
The minimal hypersurfaces in E4 are the only hypersurfaces possessing the following property: Its mean curvature vector field is harmonic. 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.
It has been shown, under certain conditions on the Gauss curvature, every totally real surface of the Cayley projective plane with parallel mean curvature vector is either flat or totally geodesic. 相似文献
8.
9.
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
10.
11.
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
12.
13.
14.
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
15.
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
16.
Xuan Hien Nguyen 《Journal of Geometric Analysis》2013,23(3):1379-1426
We describe a construction of complete embedded self-translating surfaces under mean curvature flow by desingularizing the intersection of a finite family of grim reapers in general position. 相似文献
17.
Rafael López 《Monatshefte für Mathematik》1999,76(1):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. 相似文献
18.
19.
The authors mainly study the generalized symplectic mean curvature flow in an almost Einstein surface, and prove that this flow has no type-I singularity. In the graph case, the global existence and convergence of the flow at infinity to a minimal surface with metric of the ambient space conformal to the original one are also proved. 相似文献
20.
Computational Mathematics and Mathematical Physics - This paper is devoted to the simulation of the mean curvature flow on a surface of revolution. The surface is discretized using the icosahedral... 相似文献