共查询到20条相似文献,搜索用时 250 毫秒
1.
Yong-Geun Oh 《Journal of Geometric Analysis》1997,7(2):305-327
In this paper, we study the structure ofJ-holomorphic discs in relation to the Fredholm theory of pseudo-holomorphic discs with totally real boundary conditions in
almost complex manifolds (M, J). We prove that anyJ-holomorphic disc with totally real boundary condition that is injective in the interior except at a discrete set of points,
which we call a “normalized disc,” must either have some boundary point that is regular and has multiplicity one, or satisfy
that its image forms a smooth immersed compact surface (without boundary) with a finite number of self-intersections and a
finite number of branch points. In the course of proving this theorem, we also prove several theorems on the local structure
of boundary points ofJ-holomorphic discs, and as an application we give a complete treatment of the transverslity result for Floer’s pseudo-holomorphic
trajectories for Lagrangian intersections in symplectic geometry.
This paper is supported in part by NSF Grant DMS 9215011. 相似文献
2.
David S. Metzler 《manuscripta mathematica》1999,100(3):277-289
We give a purely K-theoretic proof of a case of the “quantization commutes with reduction” result, conjectured by Guillemin and Sternberg and
proved by Meinrenken and Vergne. We show that the quantization is simply a pushforward in K-theory, and use Lerman's symplectic cutting and the localization theorem in equivariant K-theory to prove that quantization commutes with reduction. The case where G=S
1 and the action is free on the zero level set of the moment map is addressed.
Received: 9 March 1999 相似文献
3.
Denis Auroux 《Inventiones Mathematicae》2000,139(3):551-602
We show that every compact symplectic 4-manifold X can be topologically realized as a covering of ℂℙ2 branched along a smooth symplectic curve in X which projects as an immersed curve with cusps in ℂℙ2. Furthermore, the covering map can be chosen to be approximately pseudo-holomorphic with respect to any given almost-complex
structure on X.
Oblatum 9-III-1999 & 2-IX-1999 / Published online: 29 November 1999 相似文献
4.
Miaomiao Zhu 《Calculus of Variations and Partial Differential Equations》2009,35(2):169-189
We study Dirac-harmonic maps from degenerating spin surfaces with uniformly bounded energy and show the so-called generalized
energy identity in the case that the domain converges to a spin surface with only Neveu–Schwarz type nodes. We find condition
that is both necessary and sufficient for the W
1,2 × L
4 modulo bubbles compactness of a sequence of such maps.
Supported by IMPRS “Mathematics in the Sciences” and the Klaus Tschira Foundation. 相似文献
5.
V. Elser 《Discrete and Computational Geometry》2001,25(3):445-476
The level set of an elliptic function is a doubly periodic point set in ℂ. To obtain a wider spectrum of point sets, we consider,
more generally, a Riemann surface S immersed in ℂ2 and its sections (“cuts”) by ℂ More specifically, we consider surfaces S defined in terms of a fundamental surface element obtained as a conformai map of triangular domains in ℂ. The discrete group
of isometries of ℂ2 generated by reflections in the triangle edges leaves S invariant and generalizes double-periodicity. Our main result concerns the special case of maps of right triangles, with
the right angle being a regular point of the map. For this class of maps we show that only seven Riemann surfaces, when cut,
form point sets that are discrete in ℂ. Their isometry groups all have a rank 4 lattice subgroup, but only three of the corresponding
point sets are doubly periodic in ℂ. The remaining surfaces form quasiperiodic point sets closely related to the vertex sets
of quasiperiodic tilings. In fact, vertex sets of familiar tilings are recovered in all cases by applying the construction
to a piecewise flat approximation of the corresponding Riemann surface. The geometry of point sets formed by cuts of Riemann
surfaces is no less “rigid” than the geometry determined by a tiling, and has the distinct advantage in having a regular behavior
with respect to the complex parameter which specifies the cut. 相似文献
6.
M.-C. Arnaud 《Publications Mathématiques de L'IHéS》2009,109(1):1-17
A theorem due to G. D. Birkhoff states that every essential curve which is invariant under a symplectic twist map of the annulus
is the graph of a Lipschitz map. We prove: if the graph of a Lipschitz map h:T→R is invariant under a symplectic twist map, then h is a little bit more regular than simply Lipschitz (Theorem 1); we deduce that there exists a Lipschitz map h:T→R whose graph is invariant under no symplectic twist map (Corollary 2).
Assuming that the dynamic of a twist map restricted to a Lipschitz graph is bi-Lipschitz conjugate to a rotation, we obtain
that the graph is even C
1 (Theorem 3).
Then we consider the case of the C
0 integrable symplectic twist maps and we prove that for such a map, there exists a dense G
δ
subset of the set of its invariant curves such that every curve of this G
δ
subset is C
1 (Theorem 4). 相似文献
7.
Yong-Geun Oh 《纯数学与应用数学通讯》1992,45(1):121-139
We give a proof of the theorem of removing isolated singularities of pseudo-holomorphic curves with Lagrangian boundary conditions and bounded symplectic area. The proof is a combination of some Lp-type estimates, standard techniques of geometric P.D.E., and some ideas from symplectic geometry and calibration theory. 相似文献
8.
Neeta Pandey 《Proceedings Mathematical Sciences》1999,109(1):1-10
We define a class of simplicial maps — those which are “expanding directions preserving” — from a barycentric subdivision to the original simplicial complex. These maps naturally induce a self map on the links
of their fixed points. The local index at a fixed point of such a map turns out to be the Lefschetz number of the induced
map on the link of the fixed point in relative homology. We also show that a weakly hyperbolic [4] simplicial map sdnK →K is expanding directions preserving. 相似文献
9.
Benjamin Weiss 《Israel Journal of Mathematics》1989,66(1-3):364-368
We give a proof of Tucker’s Combinatorial Lemma that proves the fundamental nonexistence theorem: There exists no continuous
map fromB
n toS
n − 1 that maps antipodal points of∂B
n to antipodal points ofS
n − 1. 相似文献
10.
Alexander G. Reznikov 《Israel Journal of Mathematics》1992,80(1-2):207-224
We use the integral geometric formulas in the symplectic space of geodesics of a Riemannian manifold to derive various inequalities
of isoperimetric type. We give a sharp lower bound for the area of the minimal bubble spanning a spherical curve in ℝ3. We also present an “inverse Croke inequality” relating the area of the boundary of a complex domain in a Riemannian manifold
to the injectivity radius and the volume of the domain. We prove a sharp lower bound for the ground state of the harmonic
oscillator operator inL
2(M), whereM is a Hadamard manifold.
This article is dedicated to my dear friend Julia Rashba 相似文献
11.
Michael Hutchings 《Journal of Geometric Analysis》1997,7(2):285-304
We show that the least area required to enclose two volumes in ℝn orS
n forn ≥ 3 is a strictly concave function of the two volumes. We deduce that minimal double bubbles in ℝn have no empty chambers, and we show that the enclosed regions are connected in some cases. We give consequences for the structure
of minimal double bubbles in ℝn. We also prove a general symmetry theorem for minimal enclosures ofm volumes in ℝn, based on an idea due to Brian White.
Supported in part by NSF DMS-9409166. 相似文献
12.
13.
We formulate, for regular μ>ω, a “forcing principle” Sμ which we show is equivalent to the existence of morasses, thus providing a new and systematic method for obtaining applications
of morasses. Various examples are given, notably that for infinitek, if 2
k
=k
+ and there exists a (k
+, 1)-morass, then there exists ak
++-super-Souslin tree: a normalk
++ tree characterized by a highly absolute “positive” property, and which has ak
++-Souslin subtree. As a consequence we show that CH+SHℵ
2⟹ℵ2 is (inaccessible)L.
This author thanks the US-Israel Binational Science Foundation for partial support of this research. 相似文献
14.
Michael Entov 《Inventiones Mathematicae》2001,146(1):93-141
Given a closed symplectic manifold (M,ω) we introduce a certain quantity associated to a tuple of conjugacy classes in the universal cover of the group Ham (M,ω) by means of the Hofer metric on Ham (M,ω). We use pseudo-holomorphic curves involved in the definition of the multiplicative structure on the Floer cohomology of
a symplectic manifold (M,ω) to estimate this quantity in terms of actions of some periodic orbits of related Hamiltonian flows. As a corollary we
get a new way to obtain Agnihotri-Belkale-Woodward inequalities for eigenvalues of products of unitary matrices. As another
corollary we get a new proof of the geodesic property (with respect to the Hofer metric) of Hamiltonian flows generated by
certain autonomous Hamiltonians. Our main technical tool is K-area defined for Hamiltonian fibrations over a surface with
boundary in the spirit of L. Polterovich’s work on Hamiltonian fibrations over S
2.
Oblatum 23-II-2001 & 9-V-2001?Published online: 20 July 2001 相似文献
15.
This paper deals with sparse approximations by means of convex combinations of elements from a predetermined “basis” subsetS of a function space. Specifically, the focus is on therate at which the lowest achievable error can be reduced as larger subsets ofS are allowed when constructing an approximant. The new results extend those given for Hilbert spaces by Jones and Barron,
including, in particular, a computationally attractive incremental approximation scheme. Bounds are derived for broad classes
of Banach spaces; in particular, forL
p spaces with 1<p<∞, theO (n
−1/2) bounds of Barron and Jones are recovered whenp=2.
One motivation for the questions studied here arises from the area of “artificial neural networks,” where the problem can
be stated in terms of the growth in the number of “neurons” (the elements ofS) needed in order to achieve a desired error rate. The focus on non-Hilbert spaces is due to the desire to understand approximation
in the more “robust” (resistant to exemplar noise)L
p, 1 ≤p<2, norms.
The techniques used borrow from results regarding moduli of smoothness in functional analysis as well as from the theory of
stochastic processes on function spaces. 相似文献
16.
We propose an implicit discretization of the p-harmonic map heat flow into the sphere S
2 that enjoys a discrete energy inequality and converges under only a mild mesh constraint to a weak solution. A fully practical
iterative scheme that approximates the solution of the nonlinear system of equations in each time step is proposed and analyzed.
Computational studies to motivate possible finite-time blow-up behavior of solutions for p ≠ 2 are included.
Supported by Deutsche Forschungsgemeinschaft through the DFG Research Center Matheon “Mathematics for key technologies” in Berlin. 相似文献
17.
We construct examples of symplectic half-flat manifolds on compact quotients of solvable Lie groups. We prove that the Calabi-Yau
structures are not rigid in the class of symplectic half-flat structures. Moreover, we provide an example of a compact 6-dimensional
symplectic half-flat manifold whose real part of the complex volume form is d-exact. Finally we discuss the 4-dimensional case.
This work was supported by the Projects M.I.U.R. “Geometric Properties of Real and Complex Manifolds”, “Riemannian Metrics
and Differentiable Manifolds” and by G.N.S.A.G.A. of I.N.d.A.M. 相似文献
18.
Some inequalities for Gaussian processes and applications 总被引:3,自引:0,他引:3
Yehoram Gordon 《Israel Journal of Mathematics》1985,50(4):265-289
We present a generalization of Slepian's lemma and Fernique's theorem. We show how these can be easily applied to give a new
proof, with improved estimates, of Dvoretzky’s theorem on the existence of “almost” spherical sections for arbitrary convex
bodies inR
N, while avoiding the isoperimetric inequality.
Supported by Technion V.P.R. grant #100–526, and fund for the promotion of research at the Technion #100–559. 相似文献
19.
Patrice P. Ntumba 《Czechoslovak Mathematical Journal》2012,62(1):265-278
Like the classical Gram-Schmidt theorem for symplectic vector spaces, the sheaf-theoretic version (in which the coefficient
algebra sheaf A is appropriately chosen) shows that symplectic A-morphisms on free A-modules of finite rank, defined on a topological space X, induce canonical bases (Theorem 1.1), called symplectic bases. Moreover (Theorem 2.1), if (ℰ, φ) is an A-module (with respect to a ℂ-algebra sheaf A without zero divisors) equipped with an orthosymmetric A-morphism, we show, like in the classical situation, that “componentwise” φ is either symmetric (the (local) geometry is orthogonal) or skew-symmetric (the (local) geometry is symplectic). Theorem 2.1 reduces to the classical
case for any free A-module of finite rank. 相似文献
20.
A numerical isomorphism invariant,joining-rank, was introduced in [1] as a quantitative generalization of Rudolph’s property of minimal selfjoinings. Therein, a structure
theory was developed for those transformationsT whose joining-rank, jr (T), is finite. Here, we sharpen the theorem and show it to be canonical: If jr (T)<∞ then there is a unique triple 〈e, p, S〉 wheree andp are natural numbers andS is a map with minimal self-joinings, such thatT is ane-point extension ofS
P. Furthermore, the producte·p equals the joining-rank ofT.
This theorem applies to any finite-rank mixing map, since for such maps the rank dominates the joining-rank. Another corollary
is that any rank-1 transformation which is partial-mixing has minimal self-joinings. This partially answers a question of
[3].
Partially supported by a National Science Foundation Postdoctoral Research Fellowship. 相似文献