共查询到20条相似文献,搜索用时 15 毫秒
1.
Joaquí n Pé rez 《Transactions of the American Mathematical Society》1997,349(6):2371-2389
The spaces of nondegenerate properly embedded minimal surfaces in quotients of by nontrivial translations or by screw motions with nontrivial rotational part, fixed finite topology and planar type ends, are endowed with natural structures of finite dimensional real analytic manifolds. This nondegeneracy is defined in terms of Jacobi functions. Riemann's minimal examples are characterized as the only nondegenerate surfaces with genus one in their corresponding spaces. We also give natural immersions of these spaces into certain complex Euclidean spaces which turn out to be Lagrangian immersions with respect to the standard symplectic structures.
2.
Thomas Deck 《Annals of Global Analysis and Geometry》1994,12(1):305-312
We investigate two-dimensional timelike surfaces in a Lorentz manifold (X,g). It is shown that orientable surfaces with two spacelike boundary components (homeomorphic toS
1) are necessarily of topological type [0,1] x S1. We treat the initial value problem of a string (known from physics) as a purely geometric problem: Find a minimal surface which is specified by an initial curve and by a distribution of timelike tangent planes along . We prove the local existence and uniqueness of and also obtain global existence for special types (X,g). Global existence does not generally hold; we give a counter-example, which can be interpreted as a string collapsing into a black hole. 相似文献
3.
In this paper we prove that two lines bounding an immersed minimal surface in a slab in R
3 homeomorphic to a compact Riemann surface minus two disks and a finite number of points must be parallel. This theorem is
extended to a higher dimensional minimal hypersurface. Also it is proved that if the Gauss map of a complete embedded minimal
surface of finite total curvature at a planar end has order two, then the intersection of the surface with the plane asymptotic
to the planar end cannot admit a one-to-one orthogonal projection onto any line in the plane.
Received: November 26, 1998 相似文献
4.
Let Γ be a closed, sufficiently smooth Jordan curve in and denote by the class of disk-type surfaces which map ∂B continuously and monotonically onto Γ. Then any minimal surface possesses only finitely many branch points in , and the order of any such point is well-defined, and also the index of an interior branch point is defined in a natural way if X is nonplanar. We show that also the index of boundary branch points can be defined if the curvature κ and the torsion τ of
Γ are strictly nonzero. Secondly we derive upper bounds for the index of any branch point in terms of the total curvature
of Γ or of its cut number.
Dedicated to Professor Heinz K?nig on the occasion of his 80th birthday 相似文献
5.
Anthony J. Small 《Annals of Global Analysis and Geometry》1994,12(1):97-101
The collection of minimal herissons in
3 is endowed with a vector space structure. The existence of this structure is related to the fact that null curves inC
3 are described by a single map from the étalé space of the sheaf of germs of holomorphic sections of the line bundle of degree 2 over 1 to C3, which islinear on stalks. There is an analogous construction for null curves inC
4. This gives a similar class of minimal surfaces in 4. 相似文献
6.
Karina Olszak 《Central European Journal of Mathematics》2005,3(2):309-317
Using the one-to-one correspondence between Kähler-Norden and holomorphic Riemannian metrics, important relations between various Riemannian invariants of manifolds endowed with such metrics were established in my previous paper [19]. In the presented paper, we prove that there is a strict relation between the holomorphic Weyl and Bochner conformal curvature tensors and similarly their covariant derivatives are strictly related. Especially, we find necessary and sufficient conditions for the holomorphic Weyl conformal curvature tensor of a Kähler-Norden manifold to be holomorphically recurrent. 相似文献
7.
Let M be a helicoidal surface in E
3, free of points of vanishing Gaussian curvature. Let H be the mean curvature and K
II
the curvature of the second fundamental form. In this note it is shown that the helicoidal surfaces satisfying K
II
=H are locally characterized by constancy of the ratio of the principal curvatures. Moreover it is proved that these helicoidal
surfaces are determined by a first order differential equation.
Research supported by E.E.C. contract CHRX-CT92-0050. 相似文献
8.
A near perfect matching is a matching saturating all but one vertex in a graph. If G is a connected graph and any n independent edges in G are contained in a near perfect matching, then G is said to be defect n-extendable. If for any edge e in a defect n-extendable graph G, G−e is not defect n-extendable, then G is minimal defect n-extendable. The minimum degree and the connectivity of a graph G are denoted by δ(G) and κ(G) respectively. In this paper, we study the minimum degree of minimal defect n-extendable bipartite graphs. We prove that a minimal defect 1-extendable bipartite graph G has δ(G)=1. Consider a minimal defect n-extendable bipartite graph G with n≥2, we show that if κ(G)=1, then δ(G)≤n+1 and if κ(G)≥2, then 2≤δ(G)=κ(G)≤n+1. In addition, graphs are also constructed showing that, in all cases but one, there exist graphs with minimum degree that satisfies the established bounds. 相似文献
9.
10.
11.
Ewa Tyszkowska 《Central European Journal of Mathematics》2003,1(2):208-220
The famous theorem of Belyi states that the compact Riemann surface X can be defined over the number field if and only if
X can be uniformized by a finite index subgroup Γ of a Fuchsian triangle group Λ. As a result such surfaces are now called
Belyi surfaces. The groups PSL(2,q),q=p
n
are known to act as the groups of automorphisms on such surfaces. Certain aspects of such actions have been extensively studied
in the literature. In this paper, we deal with symmetries. Singerman showed, using acertain result of Macbeath, that such
surfaces admit a symmetry which we shall call in this paper the Macbeath-Singerman symmetry. A classical theorem by Harnack
states that the set of fixed points of a symmetry of a Riemann surface X of genus g consists of k disjoint Jordan curves called ovals for some k ranging between 0 and g+1. In this paper we show that given an odd prime p, a Macbetah-Singerman symmetry of Belyi surface with PSL(2,p) as a group of automorphisms has at most 相似文献
12.
Yong Liu Kelei Wang Juncheng Wei 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(4):993-1017
From minimal surfaces such as Simons' cone and catenoids, using refined Lyapunov–Schmidt reduction method, we construct new solutions for a free boundary problem whose free boundary has two components. In dimension 8, using variational arguments, we also obtain solutions which are global minimizers of the corresponding energy functional. This shows that the theorem of Valdinoci et al. [41], [42] is optimal. 相似文献
13.
14.
In 1992, Ross proved that some classical triply periodic minimal surfaces in three-dimensional Euclidean space (Schwarz P surface, D surface, and Schoen's gyroid) are stable for volume-preserving variations. This paper extends the result to four one-parameter families of triply periodic minimal surfaces, namely, tP family, tD family, rPD family, and H family. We obtain sufficient conditions for volume-preserving stability, and as their numerical applications, we prove that, for each family, every triply periodic minimal surface with Morse index one is volume-preserving stable. 相似文献
15.
Jesús A. Alvarez López 《Annals of Global Analysis and Geometry》1992,10(2):179-194
For a Riemannian foliation % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFXeIraaa!4094!\[\mathcal{F}\] on a compact manifold M with a bundle-like metric, the de Rham complex of M is C-splitted as the direct sum of the basic complex and its orthogonal complement. Then the basic component % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacciGae8NUdS% 2aaSbaaSqaaiaadkgaaeqaaaaa!38B9!\[\kappa _b \] of the mean curvature form of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFXeIraaa!4094!\[\mathcal{F}\] is closed and defines a class (% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFXeIraaa!4094!\[\mathcal{F}\]) in the basic cohomology that is invariant under any change of the bundle-like metric. Moreover, any element in (% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFXeIraaa!4094!\[\mathcal{F}\]) can be realized as the basic component of the mean curvature of some bundle-like metric.It is also proved that (% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFXeIraaa!4094!\[\mathcal{F}\]) vanishes iff there exists some bundle-like metric on M for which the leaves are minimal submanifolds. As a consequence, this tautness property is verified in any of the following cases: (a) when the Ricci curvature of the transverse Riemannian structure is positive, or (b) when % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFXeIraaa!4094!\[\mathcal{F}\] is of codimension one. In particular, a compact manifold with a Riemannian foliation of codimension one has infinite fundamental group. 相似文献
16.
Dieter Kratsch 《Discrete Mathematics》2009,309(6):1724-1729
A graph H has the property MT, if for all graphs G, G is H-free if and only if every minimal (chordal) triangulation of G is H-free. We show that a graph H satisfies property MT if and only if H is edgeless, H is connected and is an induced subgraph of P5, or H has two connected components and is an induced subgraph of 2P3.This completes the results of Parra and Scheffler, who have shown that MT holds for H=Pk, the path on k vertices, if and only if k?5 [A. Parra, P. Scheffler, Characterizations and algorithmic applications of chordal graph embeddings, Discrete Applied Mathematics 79 (1997) 171-188], and of Meister, who proved that MT holds for ?P2, ? copies of a P2, if and only if ??2 [D. Meister, A complete characterisation of minimal triangulations of 2K2-free graphs, Discrete Mathematics 306 (2006) 3327-3333]. 相似文献
17.
Shaoping Chang 《Journal of Geometric Analysis》2000,10(2):243-255
We study Hamiltonian stable minimal Lagrangian closed submanifolds in the standard complex projective n-space
CP
n
.It is shown that when n = 2such a surface Σis either totally geodesic or flat if the multiplicity of the Laplacian acting on C∞(Σ)is less than or equal to 6. 相似文献
18.
Martin van Gemmeren 《Compositio Mathematica》1998,112(1):17-32
In this article we prove a Chern–Lashof inequality for immersions of manifolds with H-spherical ends. Related to this inequality we discuss different types of tightness. In particular we shall prove that an immersion of a manifold with at least two H-spherical ends is tightly immersed only if the ends are of a certain geometric type (Wintgen immersion). 相似文献
19.
This paper is aimed at studying negatively curved Riemannian manifolds acted on by a Lie group of isometries with principal orbits of codimension one. The orbit space of such a manifold M is proved to be always homeomorphic to or + and this second case may occur only when either the singular orbit is a geodesic of M or when the space is simply connected. Several corollaries are given. 相似文献
20.
Olaf Müller 《Annals of Global Analysis and Geometry》2007,32(1):67-85
In this note a proof is given for global existence and uniqueness of minimal Lorentzian surface maps from a cylinder into
a large class of globally hyperbolic Lorentzian manifolds for given initial values up to the first derivatives.
The results of this article are part of my PhD thesis written at the Max-Planck institute for Mathematics in the Sciences
in Leipzig under the supervision of Prof. Jürgen Jost to whom I want to express my gratitude. 相似文献