共查询到20条相似文献,搜索用时 15 毫秒
1.
We extend the Newlander-Nirenberg theorem to manifolds with almost complex structures that have somewhat less than Lipschitz
regularity. We also discuss the regularity of local holomorphic coordinates in the integrable case, with particular attention
to Lipschitz almost complex structures. 相似文献
2.
F. Loose 《Journal of Geometric Analysis》2000,10(2):323-337
Let (X, ω) be a symplectic manifold and ι: M ? X an isotropic embedding, ι*ω = 0. The isotropie embedding theorem gives a local normal form of X in a neighborhood of M, in particular a natural potential α of ω, ?dα = ω. Now, given certain geometrical structures on M and on the symplectic normal bundle of M, in particular inducing a natural energy momentum function H in a neighborhood of M, we construct a natural complex structure J in a neighborhood of M satisfying certain initial conditions associated to the given initial data along M and satisfying the equation (in J): dc H = α. This generalizes a theorem of Guillemin-Stenzel and Lempert-Szöke in the Lagrangean case. 相似文献
3.
4.
Marilyn Daily 《Journal of Geometric Analysis》2007,17(1):75-85
An area minimizing double bubble in ℝn is given by two (not necessarily connected) regions which have two prescribed n-dimensional volumes whose combined boundary
has least (n−1)-dimensional area. The double bubble theorem states that such an area minimizer is necessarily given by a standard
double bubble, composed of three spherical caps. This has now been proven for n = 2, 3,4, but is, for general volumes, unknown
for n ≥ 5. Here, for arbitrary n, we prove a conjectured lower bound on the mean curvature of a standard double bubble. This
provides an alternative line of reasoning for part of the proof of the double bubble theorem in ℝ3, as well as some new component bounds in ℝn. 相似文献
5.
Let R(t)=P(t)/Q(t) be a quotient of real polynomials. We show that ∫exp(iR(t)) dt/t has a uniform bound with a bound depending only on the degrees of P and Q and not on their coefficients. Also
LP estimates are obtained for certain associated singular integral operators. 相似文献
6.
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
7.
Sets K in d-dimensional Euclidean space are constructed with the property that the inverse Fourier transform of the characteristic
function 1
K
is a single dyadic orthonormal wavelet. The construction is characterized by its generality in the procedure, by its computational
implementation, and by its simplicity. The general case in which the inverse Fourier transforms of the characteristic functions 1K
1, ..., 1K
L
are a family of orthonormal wavelets is treated in [27]. 相似文献
8.
Mitsuhiro Itoh 《Journal of Geometric Analysis》2005,15(1):63-81
Study of modified scalar curvatures and the modified Yamabe problem is given. An existence theorem of type of Trudinger and
Aubin is obtained. Interpreting Isotropic curvature as a certain modified scalar curvature we can extend the four-dimensional
sphere theorem of [23]. Another modified scalar curvature is used in solving open problems concerning the conjecture of self-dual
Einstein 4-manifold and the Goldberg conjecture, both being under negative Ricci condition. 相似文献
9.
We show that if the group of holomorphic automorphisms of a connected complex manifold M of dimension n is isomorphic as a
topological group equipped with the compact-open topology to the automorphism group of the unit ball B
n ⊂ ℂ
n
,then M is biholomorphically equivalent to B
n. 相似文献
10.
A measurable set Q ⊂
R
n
is a wavelet set for an expansive matrix A if F
−1
(ΧQ) is an A-dilation wavelet. Dai, Larson, and Speegle [7] discovered the existence of wavelet sets in
R
n
associated with any real n ×n expansive matrix. In this work, we construct a class of compact wavelet sets which do not contain the origin and which are,
up to a certain linear transformation, finite unions of integer translates of an integral selfaffine tile associated with
the matrix B = A
t. Some of these wavelet sets may have good potential for applications because of their tractable geometric shapes. 相似文献
11.
Baouendi M. S. Mir Nordine Rothschild Linda Preiss 《Journal of Geometric Analysis》2002,12(4):543-580
Results on finite determination and convergence of formal mappings between smooth generic submanifolds in ℂ
N
are established in this article. The finite determination result gibes sufficient conditions to guarantee that a formal map
is uniquely determined by its jet, of a preassigned order, at a point. Convergence of formal mappings for real-analytic generic
submanifolds under appropriate assumptions is proved, and natural geometric conditions are given to assure that if two germs
of such submanifolds are formally equivalent, then, they are necessarily biholomorphically equivalent. It is also shown that
if two real-algebraic hypersurfaces in ℂ
N
are biholomorphically equivalent, then, they are algebraically equivalent. All the results are first proved in the more general
context of “reflection ideals” associated to formal mappings between formal as well as real-analytic and real-algebraic manifolds. 相似文献
12.
The construction of a multiresolution analysis starts with the specification of a scale function. The Fourier transform of
this function is defined by an infinite product. The convergence of this product is usually discussed in the context of L
2(R).Here, we treat the convergence problem by viewing the partial products as probabilities, converging weakly to a probability
defined on an appropriate sequence space. We obtain a sufficient condition for this convergence, which is also necessary in
the case where the scale function is continuous. These results extend and clarify those of Cohen [2] and Hernández et al.
[4]. The method also applies to more general dilation schemes that commute with translations by
Z
d
. 相似文献
13.
If the integer translates of a function ø with compact support generate a frame for a subspace W of L 2(?),then it is automatically a Riesz basis for W, and there exists a unique dual Riesz basis belonging to W. Considerable freedom can be obtained by considering oblique duals, i.e., duals not necessarily belonging to W. Extending work by Ben-Artzi and Ron, we characterize the existence of oblique duals generated by a function with support on an interval of length one. If such a generator exists, we show that it can be chosen with desired smoothness. Regardless whether ø is polynomial or not, the same condition implies that a polynomial dual supported on an interval of length one exists. 相似文献
14.
A. Calogero 《Journal of Geometric Analysis》2000,10(4):597-622
In the context of a general lattice Γ in Rn and a strictly expanding map M which preserves the lattice, we characterize all the wavelet families. This result generalizes
the characterization of Frazier, Garrigós, Wang, and Weis about the wavelet families with Γ = Zn and M = 21. In the second part of the paper, we characterize all the MSF wavelets. Moreover, we give a constructive method
for the support of the Fourier transform of an MSF wavelet and apply this method by giving examples with particular attention
to the quincunx lattice. 相似文献
15.
We solve the Caratheodory and Kobayashi extremal problems for the open symmetrized bidisc
We prove the equality of the Caratheodory and Kobayashi distances on G and describe the extremal functions for the two problems;
they are rational of degree 1or 2.G is the first example of a non convexifiable domain for which the two distances coincide. 相似文献
16.
Demetrio Labate 《Journal of Geometric Analysis》2002,12(3):469-491
This article presents a general result from the study of shift-invariant spaces that characterizes tight frame and dual frame
generators for shift-invariant subspaces of L2(ℝn). A number of applications of this general result are then obtained, among which are the characterization of tight frames
and dual frames for Gabor and wavelet systems. 相似文献
17.
The purpose of the paper is to study the behavior at infinity of Fourier-Laplace transforms of distributions or more generally
plurisubharmonic functions u in Cn with bounds of the form
The set L∞(u) of limits of Ttu = u(t·)/t as t → +∞ is a compact T invariant subset of the set PH of plurisubharmonic functions in Cn with v(ξ) ≤H(Im ξ), ξ ∈ Cn, and equality on CRn. Here H is a supporting function associated with u, and T is chain recurrent on L∞(u). The behavior of functions in PH at CRn is studied in detail, which leads to conditions on a set M ⊂PH which guarantee that M = L∞(u) for some u as above. One can then choose u = log | F | where F is the Fourier-Laplace transform
of a distribution with compact support. 相似文献
18.
V. Yaskin 《Journal of Geometric Analysis》2006,16(4):735-745
The lower dimensional Busemann-Petty problem asks whether origin symmetric convex bodies in ℝn with smaller volume of all k-dimensional sections necessarily have smaller volume. As proved by Bourgain and Zhang, the answer
to this question is negative if k>3. The problem is still open for k = 2, 3. In this article we formulate and completely solve
the lower dimensional Busemann-Petty problem in the hyperbolic space ℍn. 相似文献
19.
In this article we give a necessary and sufficient condition for a pair of wavelet families
in L2(ℝ
n
), to arise from a pair of biorthogonal MRA’s. The condition is given in terms of simple equations involving the functions
ψℓ and
. To work in greater generality, we allow multiresolution analyses of arbitrary multiplicity, based on lattice translations
and matrix dilations. Our result extends the characterization theorem of G. Gripenberg and X. Wang for dyadic orthonormal
wavelets in L2(ℝ),and includes, as particular cases, the sufficient conditions of P. Auscher and P.G. Lemarié in the biorthogonal situation. 相似文献
20.
Luca Brandolini Alex Iosevich Giancarlo Travaglini 《Journal of Fourier Analysis and Applications》2001,7(4):359-372
Let Γ be a smooth compact convex planar curve with arc length dm and let dσ=ψ dm where ψ is a cutoff function. For Θ∈SO (2)
set σΘ(E) = σ(ΘE) for any measurable planar set E. Then, for suitable functions f in ℝ2, the inequality.
represents an average over rotations, of the Stein-Tomas restriction phenomenon. We obtain best possible indices for the
above inequality when Γ is any convex curve and under various geometric assumptions. 相似文献