共查询到20条相似文献,搜索用时 15 毫秒
1.
Y. L. Xin 《manuscripta mathematica》1993,79(1):49-71
By using concrete isoparametric maps we obtain some new equivariant harmonic maps between spheres and solve equivariant boundary
value problems for harmonic maps from unit open ballB
m+1 intoS
n.
Research partially supported by NNSFC, SFECC and ICTP. 相似文献
2.
Shyuichi Izumiya Donghe Pei María del Carmen Romero Fuster 《Proceedings of the Steklov Institute of Mathematics》2009,267(1):156-173
We define the notions of (S
t
1 × S
s
2)-nullcone Legendrian Gauss maps and S
+2-nullcone Lagrangian Gauss maps on spacelike surfaces in anti de Sitter 4-space. We investigate the relationships between
singularities of these maps and geometric properties of surfaces as an application of the theory of Legendrian/Lagrangian
singularities. By using S
+2-nullcone Lagrangian Gauss maps, we define the notion of S
+2-nullcone Gauss-Kronecker curvatures and show a Gauss-Bonnet type theorem as a global property. We also introduce the notion
of horospherical Gauss maps which have geometric properties different from those of the above Gauss maps. As a consequence,
we can say that anti de Sitter space has much richer geometric properties than the other space forms such as Euclidean space,
hyperbolic space, Lorentz-Minkowski space and de Sitter space. 相似文献
3.
Artur Avila 《Acta Mathematica》2010,205(1):5-18
We show that smooth maps are C
1-dense among C
1 volume-preserving maps. 相似文献
4.
Kazuhiro Sakai 《数学学报(英文版)》2010,26(10):1839-1846
We study the space of positively expansive differentiable maps of a compact connected C ∞ Riemannian manifold without boundary. It is proved that (i) the C1-interior of the set of positively expansive differentiable maps coincides with the set of expanding maps, and (ii) Cl-generically, a differentiable map is positively expansive if and only if it is expanding. 相似文献
5.
We give a classification of all equivelar polyhedral maps on the torus. In particular, we classify all triangulations and quadrangulations of the torus admitting a vertex transitive automorphism group. These are precisely the ones which are quotients of the regular tessellations {3,6}, {6,3} or {4,4} by a pure translation group. An explicit formula for the number of combinatorial types of equivelar maps (polyhedral and non-polyhedral) with n vertices is obtained in terms of arithmetic functions in elementary number theory, such as the number of integer divisors of n. The asymptotic behaviour for n→∞ is also discussed, and an example is given for n such that the number of distinct equivelar triangulations of the torus with n vertices is larger than n itself. The numbers of regular and chiral maps are determined separately, as well as the ones for all other kinds of symmetry. Furthermore, arithmetic properties of the integers of type p2+pq+q2 (or p2+q2, resp.) can be interpreted and visualized by the hierarchy of covering maps between regular and chiral equivelar maps or type {3,6} (or {4,4}, resp.). 相似文献
6.
Domenico Mucci 《Journal of the European Mathematical Society》2001,3(1):1-38
For vector valued maps, convergence in W
1,1 and of all minors of the Jacobian matrix in L
1 is equivalent to convergence weakly in the sense of currents and in area for graphs. We show that maps defined on domains
of dimension n≥ 3 can be approximated strongly in this sense by smooth maps if and only if the same property holds for the restriction to
a.e. 2-dimensional plane intersecting the domain.
Received April 29, 1999 / final version received July 21, 2000?Published online September 25, 2000 相似文献
7.
A class of functional equations with nonlinear iterates is discussed on the unit circle T
1. By lifting maps on T
1 and maps on the torus T
N
to Euclidean spaces and extending their restrictions to a compact interval or cube, we prove existence, uniqueness and stability
for their continuous solutions.
Supported by NSFC#10471101, TRAPOY[2002]383 and SRFDP#20050610003. 相似文献
8.
Jérôme Buzzi 《Israel Journal of Mathematics》1997,100(1):125-161
We generalize the technique of Markov Extension, introduced by F. Hofbauer [10] for piecewise monotonic maps, to arbitrary
smooth interval maps. We also use A. M. Blokh’s [1] Spectral Decomposition, and a strengthened version of Y. Yomdin’s [23]
and S. E. Newhouse’s [14] results on differentiable mappings and local entropy.
In this way, we reduce the study ofC
r
interval maps to the consideration of a finite number of irreducible topological Markov chains, after discarding a small
entropy set. For example, we show thatC
∞ maps have the same properties, with respect to intrinsic ergodicity, as have piecewise monotonic maps. 相似文献
9.
In this paper, we shall prove that Axiom A maps are dense in the space of C2 interval maps (endowed with the C2 topology). As a step of the proof, we shall prove real and complex a priori bounds for (first return maps to certain small neighborhoods of the critical points of) real analytic multimodal interval maps with non-degenerate critical points. We shall also discuss rigidity for interval maps without large bounds. Mathematics Subject Classification (2000) Primary 37E05; Secondary 37F25 相似文献
10.
We establish a necessary and sufficient topological condition for maps that are in W1,p(M, N) to be connected by continuous paths in W1,p(M, N) to maps in W1,q(M, N), q > q ≥ 1. We also obtain a necessary and sufficient topological condition under which W1,q(M, N) is strongly dense in W1,p(M, N). Several results concerning sequential weak density of smooth (or W1,q(M, N) maps in W1,p(M, N) are also proven. © 2003 Wiley Periodicals, Inc. 相似文献
11.
This paper proves a strong convergence theorem for sequences of pseudo-holomorphic maps from a Riemann surface to a symplectic
manifoldN with tamed almost complex structure. (These are the objects used by Gromov to define his symplectic invariants.) The paper
begins by developing some analytic facts about such maps, including a simple new isoperimetric inequality and a new removable
singularity theorem.
The main technique is a general procedure for renormalizing sequences of maps to obtain “bubbles on bubbles.” This is a significant
step beyond the standard renormalization procedure of Sacks and Uhlenbeck. The renormalized maps give rise to a sequence of
maps from a “bubble tree”—a map from a wedge Σ V S2 V S2 V ... →N. The main result is that the images of these renormalized maps converge in L1,2 ∪C° to the image of a limiting pseudo-holomorphic map from the bubble tree. This implies several important properties of the
bubble tree. In particular, the images of consecutive bubbles in the bubble tree intersect, and if a sequence of maps represents
a homology class then the limiting map represents this class. 相似文献
12.
Agafonov 《Discrete and Computational Geometry》2008,29(2):305-319
Abstract. A discrete analogue of the holomorphic maps z
γ
and log(z) is studied. These maps are given by Schramm's circle pattern with the combinatorics of the square grid. It is shown that
the corresponding circle patterns are imbedded and described by special separatrix solutions of discrete Painlevé equations.
Global properties of these solutions, as well as of the discrete z
γ
and log(z) , are established. 相似文献
13.
J. Korevaar 《Selecta Mathematica, New Series》1999,5(1):107-122
One considers maps F of the unit circle into itself. For maps of class C
1 or in the Sobolev class H?, the degree or winding number is equal to the sum of the series in terms of the Fourier coefficients c
n
of F (e
it
) = f (t). Here one studies the possible relation between this series (in symmetric arrangement) and the degree for arbitrary continuous
maps F. It is shown that for such maps, the series may fail to be convergent or Abel summable. If the series does converge, the
sum may have any value different from the degree of F. 相似文献
14.
By applying the theory of quasiconformal maps in measure metric spaces that was introduced by Heinonen-Koskela, we characterize
bi-Lipschitz maps by modulus inequalities of rings and maximal, minimal derivatives in Q-regular Loewner spaces. Meanwhile the sufficient and necessary conditions for quasiconformal maps to become bi-Lipschitz
maps are also obtained. These results generalize Rohde’s theorem in ℝ
n
and improve Balogh’s corresponding results in Carnot groups.
This research is supported by China NSF (Grant No. 10271077) 相似文献
15.
It is proved by purely algebraic method that weakly conformai, conformai andA
z
3
= 0 are mutually equivalent if ϕ :Ω→ℂP
n
is a non-isotropic harmonic map and the harmonic maps with isotropy order ≥3 are uniquely determined by a system of ordinary
differential equations. A method is given, by which the isotropy orders of non-isotropic harmonic maps can be computed. 相似文献
16.
Agafonov 《Discrete and Computational Geometry》2003,29(2):305-319
Abstract. A discrete analogue of the holomorphic maps z
γ
and log(z) is studied. These maps are given by Schramm's circle pattern with the combinatorics of the square grid. It is shown that
the corresponding circle patterns are imbedded and described by special separatrix solutions of discrete Painlevé equations.
Global properties of these solutions, as well as of the discrete z
γ
and log(z) , are established. 相似文献
17.
Miaomiao Zhu 《Mathematische Zeitschrift》2010,264(1):63-85
We study harmonic maps from degenerating Riemann surfaces with uniformly bounded energy and show the so-called generalized
energy identity. We find conditions that are both necessary and sufficient for the compactness in W
1,2 and C
0 modulo bubbles of sequences of such maps. 相似文献
18.
Zhiren Jin 《Inventiones Mathematicae》1992,108(1):1-10
Summary We prove several Liouville theorems for harmonic maps between certain classes of Riemannian manifolds. In particular, the results can be applied to harmonic maps from the Euclidean space (R
m
,g
0) to a large class of Riemannian manifolds. Our assumptions on the harmonic maps concern the asymptotic behavior of the maps at .Oblatum 28-XII-1990 & 11-II-1991Supported by NSF grant DMS-8610730 相似文献
19.
Yang Xuefeng 《数学学报(英文版)》1993,9(4):401-405
In this paper, we use the deformation method andG-equivariant theory to prove the existence and multiplicity of harmonic maps from an annulus to the unit sphere inℝ
3 with symmetric boundary value. In particular, we can get infinitely many homotopically different harmonic maps if the boundary
value isS
1-equivariant and nonconstant.
This research partially supported by the NNSF, P.R. China. 相似文献
20.
L. S. Efremova 《Theoretical and Mathematical Physics》2010,164(3):1208-1214
Using the notions of an Ω-function and of functions suitable for an Ω-function, we show that the space of C
1
-smooth skew products of maps of an interval such that the quotient map of each is Ω-stable in the space of C
1
-smooth maps of a closed interval into itself and has a type ≻ 2
∞
(i.e., contains a periodic orbit with the period not equal to a power of 2) can be represented as a union of four nonempty pairwise nonintersecting subspaces. We give examples of maps belonging to
each of the identified subspaces. 相似文献