共查询到20条相似文献,搜索用时 31 毫秒
1.
We prove that given a simply connected compact manifold M and a
closed manifold N, any map in the Sobolev space W
1,2(M,N) can be
approximated weakly by smooth maps between M and N.
Submitted: September 2002, Final version: November 2002. 相似文献
2.
We generalize Turaev's definition of torsion invariants of pairs (M,&\xi;), where M is a 3-dimensional manifold and &\xi; is an Euler structure on M (a non-singular vector field up to homotopy relative to ∂M and modifications supported in a ball contained in Int(M)). Namely, we allow M to have arbitrary boundary and &\xi; to have simple (convex and/or concave) tangency circles to the boundary. We prove that
Turaev's H
1(M)-equivariance formula holds also in our generalized context. Using branched standard spines to encode vector fields we show
how to explicitly invert Turaev's reconstruction map from combinatorial to smooth Euler structures, thus making the computation
of torsions a more effective one. Euler structures of the sort we consider naturally arise in the study of pseudo-Legendrian
knots (i.e.~knots transversal to a given vector field), and hence of Legendrian knots in contact 3-manifolds. We show that torsion, as
an absolute invariant, contains a lifting to pseudo-Legendrian knots of the classical Alexander invariant. We also precisely
analyze the information carried by torsion as a relative invariant of pseudo-Legendrian knots which are framed-isotopic.
Received: 3 October 2000 / Revised version: 20 April 2001 相似文献
3.
T. Lachand-Robert M.A. Peletier 《Calculus of Variations and Partial Differential Equations》2002,15(3):289-297
We study the infimum of functionals of the form among all convex functions such that . ( is a convex open subset of , and M is a given symmetric matrix.) We prove that this infimum is the smallest eigenvalue of M if is . Otherwise the picture is more complicated. We also study the case of an x-dependent matrix M.
Received: 23 February 2000/Accepted: 4 December 2000 / Published online: 5 September 2002 相似文献
4.
Mikhail Feldman Robert J. McCann 《Calculus of Variations and Partial Differential Equations》2002,15(1):81-113
Monge's problem refers to the classical problem of optimally transporting mass: given Borel probability measures on , find the measure preserving map s(x) between them which minimizes the average distance transported. Here distance can be induced by the Euclidean norm, or any
other uniformly convex and smooth norm on . Although the solution is never unique, we give a geometrical monotonicity condition singling out a particular optimal map
s(x). Furthermore, a local definition is given for the transport cost density associated to each optimal map. All optimal maps
are then shown to lead to the same transport density .
Received: 18 December 2000 / Accepted: 11 May 2001 / Published online: 19 October 2001 相似文献
5.
Let M be a two-dimensional complex manifold and let be a holomorphic map that fixes pointwise a (possibly) singular, compact, reduced and globally irreducible curve . We give a notion of degeneracy of f at a point of C. It turns out that f is non-degenerate at one point if and only if it is non-degenerate at every point of C. When f is non-degenerate on C, we define a residual index for f at each point of C. Then we prove that the sum of the indices is equal to the self-intersection number of C.
Received: 15 May 2000; in final form: 10 July 2001 / Published online: 1 February 2002 相似文献
6.
Baisheng Yan 《Calculus of Variations and Partial Differential Equations》2001,13(3):295-310
Given a number a weakly L-quasiregular map on a domain in space is a map u in a Sobolev space that satisfies almost everywhere in In this paper, we study the problem concerning linear boundary values of weakly L-quasiregular mappings in space with dimension It turns out this problem depends on the power p of the underlying Sobolev space. For p not too far below the dimension n we show that a weakly quasiregular map in can only assume a quasiregular linear boundary value; however, for all and , we prove a rather surprising existence result that every linear map can be the boundary value of a weakly L-quasiregular map in
Received July 20, 2000 / Accepted September 22, 2000 / Published online December 8, 2000 相似文献
7.
Jan Jaworowski 《Journal of Fixed Point Theory and Applications》2007,1(1):111-121
Suppose that G is a compact Lie group, M and N are orientable, free G-manifolds and f : M → N is an equivariant map. We show that the degree of f satisfies a formula involving data given by the classifying maps of the orbit spaces M/G and N/G. In particular, if the generator of the top dimensional cohomology of M/G with integer coefficients is in the image of the cohomology map induced by the classifying map for M, then the degree is one.
The condition that the map be equivariant can be relaxed: it is enough to require that it be “nearly equivariant”, up to a
positive constant. We will also discuss the G-average construction and show that the requirement that the map be equivariant can be replaced by a somewhat weaker condition
involving the average of the map.
These results are applied to maps into real, complex and quaternionic Stiefel manifolds. In particular, we show that a nearly
equivariant map of a complex or quaternionic Stiefel manifold into itself has degree one.
Dedicated to the memory of Jean Leray 相似文献
8.
We study the question: which integers k can be realized as the degree of a map between two given closed (n-1)-connected 2n-manifolds?
Mathematics Subject Classification (2000): 57R19, 55M25
Received: 9 July 2001; in final form: 21 July 2002 //Published online: 24 February 2003 相似文献
9.
J. Schoißengeier 《Monatshefte für Mathematik》2000,131(3):227-234
For a real number x let be the fractional part of x and for any set M let c
M
be the characteristic function of M. For and a positive integer N let
be the discrepancy of the sequence modulo 1. In this paper we prove that
(Received 2 May 2000; in revised form 19 June 2000) 相似文献
10.
Let M be a geometrically finite pinched negatively curved Riemannian manifold with at least one cusp. Inspired by the theory of
Diophantine approximation of a real (or complex) number by rational ones, we develop a theory of approximation of geodesic
lines starting from a given cusp by ones returning to it. We define a new invariant for M, theHurwitz constant of M. It measures how well all geodesic lines starting from the cusp are approximated by ones returning to it. In the case of
constant curvature, we express the Hurwitz constant in terms of lengths of closed geodesics and their depths outside the cusp
neighborhood. Using the cut locus of the cusp, we define an explicit approximation sequence for a geodesic line starting from
the cusp and explore its properties. We prove that the modular once-punctured hyperbolic torus has the minimum Hurwitz constant
in its moduli space.
Received: 24 October 2000; in final form: 10 November 2001 / Published online: 17 June 2002 相似文献
11.
Let M be a map on a surface S. The edge-width of M is the length of a shortest noncontractible cycle of M. The face-width (or, representativity) of M is the smallest number of intersections a noncontractible curve in S has with M. (The edge-width and face-width of a planar map may be defined to be infinity.) A map is a large-edge-width embedding (LEW-embedding) if its maximum face valency is less than its edge-width. For several families of rooted maps on a given surface, we prove that there are positive constants C1 and C2, depending on the family and the surface, such that
- 1 almost all maps with n edges have face-width and edge-width greater than c1 log n, and
- 2 the fraction of such maps that are LEW-embeddings and the fraction that are not LEW-embeddings both exceed n? >C2.
12.
For a Lie groupoid G with a twisting σ (a PU(H)-principal bundle over G), we use the (geometric) deformation quantization techniques supplied by Connes tangent groupoids to define an analytic index morphism in twisted K-theory. In the case the twisting is trivial we recover the analytic index morphism of the groupoid.For a smooth foliated manifold with twistings on the holonomy groupoid we prove the twisted analog of the Connes–Skandalis longitudinal index theorem. When the foliation is given by fibers of a fibration, our index coincides with the one recently introduced by Mathai, Melrose, and Singer.We construct the pushforward map in twisted K-theory associated to any smooth (generalized) map f:W→M/F and a twisting σ on the holonomy groupoid M/F, next we use the longitudinal index theorem to prove the functoriality of this construction. We generalize in this way the wrong way functoriality results of Connes and Skandalis when the twisting is trivial and of Carey and Wang for manifolds. 相似文献
13.
F. Tovena 《Geometriae Dedicata》2009,139(1):15-31
Let M be a smooth complex manifold, and S(⊂ M) be a compact irreducible subvariety with dim
C
S > 0. Let be given either a holomorphic map f : M → M with f
|S
= id
S
, f ≠ id
M
, or a holomorphic foliation on M: we describe an approach that can be applied to both map and foliation in order to obtain index theorems.
Partially supported by GNSAGA, Centro de Giorgi, M.U.R.S.T. 相似文献
14.
Irene Sabadini Daniele C. Struppa Frank Sommen Peter Van Lancker 《Mathematische Zeitschrift》2002,239(2):293-320
In this paper we study complexes of k Dirac operators (or variations of Dirac operators) in the real or complex Clifford algebras i.e. complexes in which the first map is induced by the matrix where is the Dirac operator with respect to the variable . In particular we prove that, if , the complex in the case of 3 operators can be described in terms of relations coming from the so called radial algebra. Moreover we show that if the dimension m is less than 2k-1, then the Fischer decomposition does not hold.
Received: 2 February 2000; in final form: 20 June 2000 / Published online: 25 June 2001 相似文献
15.
Let M be a smooth compact orientable pseudoconvex C R manifold of real dimension three and assume that there is a smooth function λ which is strictly subharmonic in any direction where the Levi-form vanishes on M. Then we extend the given C R structure on M to an integrable almost complex structure on the concave side of M. As an application, if M is a non-compact pseudoconvex C R manifold of real dimension three, we prove that the given C R structure on M can be locally extended to an integrable almost complex structure on the concave side of M.
Partially supported by Korea research foundation Grant (KRF-2001-015-DP0016) and by R14-2002-044-01000-0 from KRF 相似文献
16.
Let M be an n-dimensional complete non-compact submanifold in a hyperbolic space with the norm of its mean curvature vector bounded by
a constant . We prove in this paper that . In particular when M is minimal we have and this is sharp because equality holds when M is totally geodesic.
Received September 14, 1999; in final form November 12, 1999 / Published online December 8, 2000 相似文献
17.
J.F. Brock 《Geometric And Functional Analysis》2000,10(4):741-797
A measured lamination μ geodesically realized in a hyperbolic 3-manifold M has a well-defined average length, due to W. Thurston. For we prove that the function measuring the average length of the maximal realizable sublamination of μ varies bicontinuously in M and μ. Since connected, positive, non-realizable measured laminations arise as zeros of the length function, its continuity suggests
new behavioral features of quasi-isometry invariants under limits of hyperbolic 3-manifolds.
Submitted: November 1998, Revised version: February 2000, Final version: May 2000. 相似文献
18.
The distributional k-dimensional Jacobian of a map u in the Sobolev space W1,k-1 which takes values in the the sphere Sk-1 can be viewed as the boundary of a rectifiable current of codimension k carried by (part of) the singularity of u which is topologically relevant. The main purpose of this paper is to investigate the range of the Jacobian operator; in particular, we show that any boundary M of codimension k can be realized as Jacobian of a Sobolev map valued in Sk-1. In case M is polyhedral, the map we construct is smooth outside M plus an additional polyhedral set of lower dimension, and can be used in the constructive part of the proof of a -convergence result for functionals of Ginzburg-Landau type, as described in [2]. Mathematics Subject Classification (2000) 46E35 (53C65, 49Q15, 26B10, 58A25) 相似文献
19.
Let M be a complete open n-manifold with a base point p, at which the radial sectional curvature along every minimizing geodesic emanating from p is bounded below by the radial curvature function of a model surface. We discuss the maximal diameter theorem for the compactification
of M by attaching the ideal boundary. Under certain conditions we prove that p becomes a pole and that M is isometric to the n-model.
Received: 24 September 2000; in final form: 21 November 2001 / Published online: 17 June 2002
Dedicated to Professor Su Bu-Chin on the occasion of his one hundredth birthday
The work of the first author was partially supported by the Grant-in-Aid for Scientific Research, No. 12440021 and for Exploratory
Research, No. 13874012 相似文献
20.
R.F. Goldin 《Geometric And Functional Analysis》2002,12(3):567-583
Let G be a compact torus acting on a compact symplectic manifold M in a Hamiltonian fashion, and T a subtorus of G. We prove that the kernel of is generated by a small number of classes satisfying very explicit restriction properties. Our main tool is the equivariant Kirwan map, a natural map from the G-equivariant cohomology of M to the G/T-equivariant cohomology of the symplectic reduction of M by T . We show this map is surjective. This is an equivariant version of the well-known result that the (nonequivariant) Kirwan
map is surjective. We also compute the kernel of the equivariant Kirwan map, generalizing the result due to Tolman and Weitsman
[TW] in the case T = G and allowing us to apply their methods inductively. This result is new even in the case that dim T = 1. We close with a worked example: the cohomology ring of the product of two , quotiented by the diagonal 2-torus action.
Submitted: September 2001, Revised: December 2001, Revised: February 2002. 相似文献