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1.
Let ƒ: D → D′ be a proper holomorphic mapping between bounded domains D, D′ in ℂ2.Let M, M′ be open pieces on δD, δD′, respectively that are smooth, real analytic and of finite type. Suppose that the cluster
set of M under ƒ is contained in M′. It is shown that ƒ extends holomorphically across M. This can be viewed as a local version
of the Diederich-Pinchuk extension result for proper mappings in ℂ2. 相似文献
2.
Let D, D′ ⊂ ℂn be bounded domains with smooth real analytic boundaries and ƒ: D → D′ be a proper holomorphic map. Our main result implies
that if the graph of ƒ extends as an analytic set to a neighborhood of a poìnt (a, a′) ∈ ∂D × 3D′ with a′ ∈ clƒ(a), then ƒ extends holomorphically to a neighborhood of a. 相似文献
3.
In this paper we describe logarithmic moduli spaces of pairs (S, D) consisting of a minimal surface S of class VII with second Betti number b
2 > 0 together with a reduced maximal divisor D of b
2 rational curves. The special case of Enoki surfaces has already been considered by Dloussky and Kohler. We use normal forms
for the action of the fundamental group of S\D and for the associated holomorphic contraction .
Part of this work was done while the first author visited the University of Osnabrück under the program “Globale Methoden
in der komplexen Geometrie” of the DFG and while the second author visited the Max-Planck-Institut für Mathematik in Bonn
and the LATP, Université de Provence. We thank these institutions for their hospitality and for financial support. Furthermore
the authors wish to thank Georges Dloussky for numerous discussions on surfaces of class VII. 相似文献
4.
O. N. Biryukov 《Journal of Mathematical Sciences》2007,146(1):5483-5489
We consider homeomorphisms ƒ of a punctured 2-disk D
2 \ P, where P is a finite set of interior points of D
2, which leave the boundary points fixed. Any such homeomorphism induces an automorphism ƒ
* of the fundamental group of D
2 \ P. Moreover, to each homeomorphism ƒ, a matrix B
ƒ (t) from GL(n, ℤ[t, t
−1]) can be assigned by using the well-known Burau representation. The purpose of this paper is to find a nontrivial lower bound
for the topological entropy of ƒ. First, we consider the lower bound for the entropy found by R. Bowen by using the growth rate of the induced automorphism
ƒ
*. Then we analyze the argument of B. Kolev, who obtained a lower bound for the topological entropy by using the spectral radius
of the matrix B
ƒ (t), where t ∈ ℂ, and slightly improve his result.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 5, pp. 47–55, 2005. 相似文献
5.
We say that a subset of Cn is hypoconvex if its complement is the union of complex hyperplanes. We say it is strictly hypoconvex if it is smoothly bounded
hypoconvex and at every point of the boundary the real Hessian of its defining function is positive definite on the complex
tangent space at that point. Let Bn be the open unit ball in Cn.Suppose K is a C∞ compact manifold in ∂B1 × Cn, n > 1, diffeomorphic to ∂B1 × ∂Bn, each of whose fibers Kz over ∂B1 bounds a strictly hypoconvex connected open set. Let K be the polynomialhull of K. Then we show that K∖K is the union of
graphs of analytic vector valued functions on B1. This result shows that an unnatural assumption regarding the deformability of K in an earlier version of this result is
unnecessary. Next, we study an H∞ optimization problem. If pis a C∞ real-valued function on ∂B1× Cn, we show that the infimum γρ = infƒ∈H
∞ (B1)n ‖ρ(z, ƒ (z))‖∞ is attained by a unique bounded ƒ provided that the set (z, w) ∈ ∂B1 × C n|ρ(z, w) ≤ γρ has bounded connected strictly hypoconvex fibers over the circle. 相似文献
6.
Flavia Giannetti Tadeusz Iwaniec Jani Onninen Anna Verde 《Journal of Geometric Analysis》2002,12(2):223-254
Let ƒ: Ω → ℝn be a mapping in the Sobolev space W1,n−1(Ω,ℝn), n ≥ 2. We assume that the determinant of the differential matrix Dƒ (x) is nonnegative, while the cofactor matrix D#ƒ satisfies
, where Lp(Ω) is an Orlicz space. We show that, under the natural Divergence Condition on P, see (1.10), the Jacobian lies in L
loc
1
(Ω). Estimates above and below L
loc
1
(Ω) are also studied. These results are stronger than the previously known estimates, having assumed integrability conditions
on the differential matrix. 相似文献
7.
We show that ifG is a semisimple algebraic group defined overQ and Γ is an arithmetic lattice inG:=G
R with respect to theQ-structure, then there exists a compact subsetC ofG/Γ such that, for any unipotent one-parameter subgroup {u
t} ofG and anyg∈G, the time spent inC by the {u
t}-trajectory ofgΓ, during the time interval [0,T], is asymptotic toT, unless {g
−1utg} is contained in aQ-parabolic subgroup ofG. Some quantitative versions of this are also proved. The results strengthen similar assertions forSL(n,Z),n≥2, proved earlier in [5] and also enable verification of a technical condition introduced in [7] for lattices inSL(3,R), which was used in our proof of Raghunathan’s conjecture for a class of unipotent flows, in [8]. 相似文献
8.
E. G. Goluzina 《Journal of Mathematical Sciences》2006,137(3):4774-4779
The paper studies the region of values Dm,1(T) of the system {ƒ(z1), ƒ(z2), …, ƒ(zm), ƒ(r)}, m e 1, where zj (j = 1, 2, …,m) are arbitrary fixed points of the disk U = {z: |z| < 1} with Im zj ≠ 0 (j = 1, 2, …,m), and r, 0 < r < 1, is fixed, in the class T of functions ƒ(z) = z+a2z2+ ⋯ regular in the disk U and satisfying in the latter the condition Im ƒ(z) Imz > 0 for Im z ≠ 0. An algebraic characterization of the set Dm,1(T) in terms of nonnegative-definite Hermitian forms is given, and all the boundary functions are described. As an implication,
the region of values of ƒ(zm) in the subclass of functions from the class T with prescribed values ƒ(zk) (k = 1, 2, …,m − 1) and ƒ(r) is determined. Bibliography: 5 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 24–33. Original article submitted June 13, 2005. 相似文献
9.
Takeshi Isobe 《Journal of Geometric Analysis》1998,8(1):43-64
Concerning the Yang-Mills functional over
R
5 ∖ {a
1,...,a
p
},we calculate its energy using geometrical term. Moreover, we may find the energy gap phenomenon with respect to the Yang-Mills
energy which occurs also for harmonic mapping etc. From this, we propose to consider new functional, called relaxed energy. 相似文献
10.
In this paper we study the order of growth of the uniform norm of the hyperinterpolation operator on the unit sphere S
r−1
⊂ Rr. The hyperinterpolation approximation L
n
ƒ, where ƒ ∈ C(S
r
−1), is derived from the exact L
2 orthogonal projection Π ƒ onto the space P
n
r
(S
r
−1) of spherical polynomials of degree n or less, with the Fourier coefficients approximated by a positive weight quadrature rule that integrates exactly all polynomials
of degree ≤ 2n. We extend to arbitrary r the recent r = 3 result of Sloan and Womersley [9], by proving that under an additional “quadrature regularity” assumption on the quadrature
rule, the order of growth of the uniform norm of the hyperinterpolation operator on the unit sphere is O(n
r
/2−1), which is the same as that of the orthogonal projection Πn, and best possible among all linear projections onto P
n
r
(S
r
−1). 相似文献
11.
Franc Forstneric 《Journal of Geometric Analysis》1999,9(1):93-117
Let n > 1 and let
C
n
denote the complex n-dimensional Euclidean space. We prove several jet-interpolation results for nowhere degenerate entire
mappings F:C
n →C
n
and for holomorphic automorphisms of
C
n
on discrete subsets of
C
n.We also prove an interpolation theorem for proper holomorphic embeddings of Stein manifolds into
C
n.For each closed complex submanifold (or subvariety) M ⊂
C
n
of complex dimension m < n we construct a domain Ω ⊂C
n
containing M and a biholomorphic map F: Ω →
C
n
onto
C
n
with J F ≡ 1such that F(M) intersects the image of any nondegenerate entire map G:C
n−m →C
n
at infinitely many points. If m = n − 1, we construct F as above such that
C
n ∖F(M) is hyperbolic. In particular, for each m ≥ 1we construct proper holomorphic embeddings F:C
m →C
m−1
such that the complement
C
m+1 ∖F(C
m
)is hyperbolic. 相似文献
12.
Letk be any field andG a finite group. Given a cohomology class α∈H
2(G,k
*), whereG acts trivially onk
*, one constructs the twisted group algebrak
αG. Unlike the group algebrakG, the twisted group algebra may be a division algebra (e.g. symbol algebras, whereG⋞Z
n×Zn). This paper has two main results: First we prove that ifD=k
α
G is a division algebra central overk (equivalentyD has a projectivek-basis) thenG is nilpotent andG’ the commutator subgroup ofG, is cyclic. Next we show that unless char(k)=0 and
, the division algebraD=k
α
G is a product of cyclic algebras. Furthermore, ifD
p is ap-primary factor ofD, thenD
p is a product of cyclic algebras where all but possibly one are symbol algebras. If char(k)=0 and
, the same result holds forD
p, p odd. Ifp=2 we show thatD
2 is a product of quaternion algebras with (possibly) a crossed product algebra (L/k,β), Gal(L/k)⋞Z
2×Z2n. 相似文献
13.
LetR be a commutative noetherian ring and ƒ1, …, ƒr ∃ R. In this article we give (cf. the Theorem in §2) a criterion for ƒ1, …, ƒr to be regular sequence for a finitely generated module overR which strengthens and generalises a result in [2]. As an immediate consequence we deduce that if V(g
1, …,g
r
) ⊆ V(ƒ1, …, ƒr) in SpecR and if ƒ1, …, ƒr is a regular sequence inR, theng
1, …,g
r is also a regular sequence inR. 相似文献
14.
TAOYOUSHAN GAOGUOZHU 《高校应用数学学报(英文版)》1998,13(3):271-280
In this paper the forced neutral difterential equation with positive and negative coefficients d/dt [x(t)-R(t)x(t-r)] P(t)x(t-x)-Q(t)x(t-σ)=f(t),t≥t0,is considered,where f∈L^1(t0,∞)交集C([t0,∞],R^ )and r,x,σ∈(0,∞),The sufficient conditions to oscillate for all solutions of this equation are studied. 相似文献
15.
LetD be a division ring with a centerC, andD[X
1, …,X
N] the ring of polynomials inN commutative indeterminates overD. The maximum numberN for which this ring of polynomials is primitive is equal to the maximal transcendence degree overC of the commutative subfields of the matrix ringsM
n(D),n=1, 2, …. The ring of fractions of the Weyl algebras are examples where this numberN is finite. A tool in the proof is a non-commutative version of one of the forms of the “Nullstellensatz”, namely, simpleD[X
1, …,X
m]-modules are finite-dimensionalD-spaces.
This paper was written while the authors were Fellows of the Institute for Advanced Studies, The Hebrew University of Jerusalem,
Mount Scopus, Jerusalem, Israel. 相似文献
16.
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
17.
We generalize a theorem of Ky Fan about the nearest distance between a closed convex set D in a Banach space E and its image by a function ƒ:D→E, in several directions: (1) for noncompact sets D, when ƒ(D) precompact; (2) for compact D and upper semicontinuous multifunction ƒ and more generally, (3) for noncompact D and upper semicontinuous multifunction ƒ with ƒ(D) Hausdorff precompact.
In particular, we prove a version of the fixed point theorem of Kakutani-Ky Fan for multifunctions whose values are convex
closed bounded, thus not necessarily compact.
Received May 23, 2000, Accepted September 4, 2001 相似文献
18.
Edoardo Ballico 《Monatshefte für Mathematik》1993,115(1-2):13-26
Here we study the real locus (i.e. the fixed locus by the conjugation) of a few moduli spaces (defined overR) of complex objects (essentially moduli spaces of surfaces of general type or of vector bundles on curves andP
2). 相似文献
19.
The motivation for this paper comes from the Halperin–Carlsson conjecture for (real) moment-angle complexes. We first give
an algebraic combinatorics formula for the M?bius transform of an abstract simplicial complex K on [m]={1,…,m} in terms of the Betti numbers of the Stanley–Reisner face ring k(K) of K over a field k. We then employ a way of compressing K to provide the lower bound on the sum of those Betti numbers using our formula. Next we consider a class of generalized moment-angle
complexes
ZK(\mathbb D, \mathbb S)\mathcal{Z}_{K}^{(\underline{\mathbb{ D}}, \underline{\mathbb{ S}})}, including the moment-angle complex ZK\mathcal{Z}_{K} and the real moment-angle complex
\mathbbRZK\mathbb{R}\mathcal {Z}_{K} as special examples. We show that
H*(ZK(\mathbb D, \mathbb S);k)H^{*}(\mathcal{Z}_{K}^{(\underline{\mathbb{ D}}, \underline{\mathbb{ S}})};\mathbf{k}) has the same graded k-module structure as Tor
k[v](k(K),k). Finally we show that the Halperin–Carlsson conjecture holds for ZK\mathcal{Z}_{K} (resp.
\mathbb RZK\mathbb{ R}\mathcal{Z}_{K}) under the restriction of the natural T
m
-action on ZK\mathcal{Z}_{K} (resp. (ℤ2)
m
-action on
\mathbb RZK\mathbb{ R}\mathcal{Z}_{K}). 相似文献
20.
François Lauze 《manuscripta mathematica》1997,92(1):525-543
Letk be an algebraically closed field,P
n
the n-dimensional projective space overk andT
P
n
the tangent vector bundle ofP
n
. In this paper I prove the following result: for every integerl, for every non-negative integers, ifZ
s
is the union ofs points in sufficiently general position inP
n
, then the restriction mapH
0(P
n
,T
P
n
(l)) →H
0(Z
s,T
P
n
(l)|z
s
) has maximal rank. This result implies that the last non-trivial term of the minimal free resolution of the homogeneous ideal
ofZ
s is the conjectured one by the Minimal Resolution Conjecture of Anna Lorenzini (cf. [Lo]). 相似文献