共查询到20条相似文献,搜索用时 671 毫秒
1.
Kenneth D. Koenig 《Mathematische Annalen》2007,339(3):667-693
We prove that the difference between the Bergman and Szegö projections on a bounded, pseudoconvex domain (with C ∞ boundary) is smoothing whenever the boundary Laplacian is subelliptic. An equivalent statement is that the Bergman projection can be represented as a composition of the Szegö and harmonic Bergman projections (along with the restriction and Poisson extension operators) modulo an error that is smoothing. We give several applications to the study of optimal mapping properties for these projections and their difference. 相似文献
2.
Kaushal Verma 《Mathematische Annalen》2009,344(3):645-701
Let D be a bounded domain in C
2 with a non-compact group of holomorphic automorphisms. Model domains for D are obtained under the hypotheses that at least one orbit accumulates at a boundary point near which the boundary is smooth,
real analytic and of finite type.
The author was supported by DST (India) Grant No.: SR/S4/MS-283/05 and in part by a grant from UGC under DSA-SAP, Phase IV. 相似文献
3.
We prove that a backward orbit with bounded Kobayashi step for a hyperbolic, parabolic or strongly elliptic holomorphic self-map of a bounded strongly convex C2 domain in Cd necessarily converges to a repelling or parabolic boundary fixed point, generalizing previous results obtained by Poggi-Corradini in the unit disk and by Ostapyuk in the unit ball of Cd. 相似文献
4.
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
5.
Tiba 《Applied Mathematics and Optimization》2008,47(1):45-58
Abstract. We prove that for bounded open sets Ω with continuous boundary, Sobolev spaces of type W
0
l,p
(Ω ) are characterized by the zero extension outside of Ω . Combining this with a compactness result for domains of class C, we obtain a general existence theorem for shape optimization problems governed by nonlinear nonhomogenous Dirichlet boundary
value problems of arbitrary order, in arbitrary dimension and with general cost functionals. 相似文献
6.
Michael L. Mihalik 《Commentarii Mathematici Helvetici》1996,71(1):362-372
If a finitely presented groupG is negatively curved, automatic or asynchronously automatic thenG has an asynchronously bounded “almost prefix closed” combing. Results in [Br1] and [E] imply that the fundamental group of any closed 3-manifold satisfying Thurston's geometrization conjecture has an
asynchronously bounded, almost prefix closed combing.
MAIN THEOREM. IfM is a compactP
2-irreducible 3-manifold,π
1 (M) has an asynchronously bounded, almost prefix closed combing, andH, a subgroup ofπ
1 (M), is quasiconvex with respect to this combing, then the cover ofM corresponding toH is a missing boundary manifold. 相似文献
7.
Tiba 《Applied Mathematics and Optimization》2003,47(1):45-58
Abstract. We prove that for bounded open sets Ω with continuous boundary, Sobolev spaces of type W
0
l,p
(Ω ) are characterized by the zero extension outside of Ω . Combining this with a compactness result for domains of class C, we obtain a general existence theorem for shape optimization problems governed by nonlinear nonhomogenous Dirichlet boundary
value problems of arbitrary order, in arbitrary dimension and with general cost functionals. 相似文献
8.
Xiangsheng Xu 《偏微分方程通讯》2013,38(1-2):199-213
Abstract We show the existence of weak solutions in an elliptic region in the self-similar plane to the two-dimensional Riemann problem for the pressure-gradient system of the compressible Euler system. The two-dimensional Riemann problem we study is the interaction of two forward rarefaction waves, which are adjacent to a common vacuum that occupies a sectorial domain of 90 degrees. We assume the origin is on the boundary of the domain. In addition, the domain is open, bounded, and simply connected with a piecewise C 2,α boundary. We resolve the difficulty that arises from the fact that the origin is on the boundary of the domain. 相似文献
9.
Hidetaka Hamada 《Journal of Geometric Analysis》1998,8(3):441-446
The purpose of this paper is to prove that every proper holomorphic self-mapping of a Reinhardt domain Ω in
C
n
which is a generalization of a complex ellipsoid is biholomorphic. The main novelty of our result is that Ω is a domain in
C
n
such that it is allowed to have a boundary point at which the Levi determinant has infinite order of vanishing. 相似文献
10.
Bao Fu Wang 《数学学报(英文版)》2009,25(8):1353-1362
Given a bounded convex domain Ω with C∞ boundary and a function ψ∈C∞(δΩ), Li-Simon-Chen can construct an Euclidean complete and W-complete convex hypersurface M with constant affine Gauss-Kronecker curvature, and they guess the M is also affine complete. In this paper, we give a confirmation answer. 相似文献
11.
Imre Patyi 《Bulletin des Sciences Mathématiques》2011,(3):43
Let X be a separable Banach space and u:X→R locally upper bounded. We show that there are a Banach space Z and a holomorphic function h:X→Z with u(x)<‖h(x)‖ for x∈X. As a consequence we find that the sheaf cohomology group Hq(X,O) vanishes if X has the bounded approximation property (i.e., X is a direct summand of a Banach space with a Schauder basis), O is the sheaf of germs of holomorphic functions on X, and q?1. As another consequence we prove that if f is a C1-smooth -closed (0,1)-form on the space X=L1[0,1] of summable functions, then there is a C1-smooth function u on X with on X. 相似文献
12.
Péter Simon 《Monatshefte für Mathematik》2000,131(4):321-334
The one- and two-parameter Walsh system will be considered in the Paley as well as in the Kaczmarz rearrangement. We show
that in the two-dimensional case the restricted maximal operator of the Walsh–Kaczmarz (C, 1)-means is bounded from the diagonal Hardy space H
p
to L
p
for every . To this end we consider the maximal operator T of a sequence of summations and show that the p-quasi-locality of T implies the same statement for its two-dimensional version T
α. Moreover, we prove that the assumption is essential. Applying known results on interpolation we get the boundedness of T
α as mapping from some Hardy–Lorentz spaces to Lorentz spaces. Furthermore, by standard arguments it will be shown that the
usual two-parameter maximal operators of the (C, 1)-means are bounded from L
p
spaces to L
p
if . As a consequence, the a.e. convergence of the (C, 1)-means will be obtained for functions such that their hybrid maximal function is integrable. Of course, our theorems from
the two-dimensional case can be extended to higher dimension in a simple way.
(Received 20 April 2000; in revised form 25 September 2000) 相似文献
13.
Burglind Jöricke 《Journal of Geometric Analysis》1999,9(2):257-300
Let Ω be a bounded strictly pseudoconvex domain in ℂn, n ≥ 3, with boundary ∂Ω, of class C2. A compact subset K is called removable if any analytic function in a suitable small neighborhood of ∂Ω K extends to an analytic
function in Ω. We obtain sufficient conditions for removability in geometric terms under the condition that K is contained
in a generic C2 -submanifold M of co-dimension one in ∂Ω. The result uses information on the global geometry of the decomposition of a CR-manifold
into CR-orbits, which may be of some independent interest. The minimal obstructions for removability contained in M are compact
sets K of two kinds. Either K is the boundary of a complex variety of co-dimension one in Ω or it is an exceptional minimal
CR-invariant subset of M, which is a certain analog of exceptional minimal sets in co-dimension one foliations. It is shown
by an example that the latter possibility may occur as a nonremovable singularity set.
Further examples show that the germ of envelopes of holomorphy of neighborhoods of ∞Ω K for K ⊂ M may be multisheeted. A couple
of open problems are discussed. 相似文献
14.
Huiling Le 《Probability Theory and Related Fields》1996,106(1):137-149
Summary. Suppose that M is a complete, simply connected Riemannian manifold of non-positive sectional curvature with dimension m ≧ 3. If, outside a fixed compact set, the sectional curvatures are bounded above by a negative constant multiple of the inverse
of the square of the geodesic distance from a fixed point and below by another negative constant multiple of the square of
the geodesic distance, then the angular part of Brownian motion on M tends to a limit as time tends to infinity, and the closure of the support of the distribution of this limit is the entire
S
m−1
. This improves a result of Hsu and March.
Received: 7 December 1994/In revised form: 2 September 1995 相似文献
15.
The Picard variety Pic0(?
n
) of a complex n-dimensional torus?
n
is the group of all holomorphic equivalence classes of topologically trivial holomorphic (principal) line bundles on ?
n
. The total space of a topologically trivial holomorphic (principal) line bundle on a compact K?hler manifold is weakly pseudoconvex.
Thus we can regard Pic0(?
n
) as a family of weakly pseudoconvex K?hler manifolds. We consider a problem whether the Kodaira's -Lemma holds on a total space of holomorphic line bundle belonging to Pic0(?
n
). We get a criterion for this problem using a dynamical system of translations on Pic0(?
n
). We also discuss the problem whether the -Lemma holds on
strongly pseudoconvex K?hler manifolds or not. Using the result of ColColţoiu, we find a 1-convex complete K?hler manifold
on which the -Lemma does not hold.
Received: 11 June 1999 / Revised version: 22 November 1999 相似文献
16.
We prove that a linear bounded extension operator exists for the trace of C
1·ω (R
n
)to an arbitrary closed subset of
R
n
.The similar result is obtained for some other spaces of multivariate smooth functions. We also show that unlike the one-dimensional
case treated by Whitney, for some trace spaces of multivariate smooth functions a linear bounded extension operator does not
exist. The proofs are based on a relation between the problem under consideration and a similar problem for Lipschitz spaces
defined on hyperbolic Riemannian manifolds. 相似文献
17.
In this paper we show the existence of two principal eigenvalues associated to general non-convex fully nonlinear elliptic
operators with Neumann boundary conditions in a bounded C
2 domain. We study these objects and we establish some of their basic properties. Finally, Lipschitz regularity, uniqueness
and existence results for the solution of the Neumann problem are given.
相似文献
18.
We introduce two new types of Dehn functions of group presentations which seem more suitable (than the standard Dehn function)
for infinite group presentations and prove the fundamental equivalence between the solvability of the word problem for a group
presentation defined by a decidable set of defining words and the property of being computable for one of the newly introduced
functions (this equivalence fails for the standard Dehn function). Elaborating on this equivalence and making use of this
function, we obtain a characterization of finitely generated groups for which the word problem can be solved in nondeterministic
polynomial time.
We also give upper bounds for these functions, as well as for the standard Dehn function, for two well-known periodic groups.
In particular, we prove that the (standard) Dehn function of a 2-group Γ of intermediate growth, defined by a system of defining
relators due to Lysenok, is bounded from above by C1x2 log2 x, where C1 > 1 is a constant. We also show that the (standard) Dehn function of a free m-generator Burnside group B(m, n) of exponent n ≥ 248, where n is either odd or divisible by 29, defined by a minimal system of defining relators, is bounded from above by the subquadratic function x19/12.
Received: September 2007, Revision: March 2008, Accepted: March 2008 相似文献
19.
Miroslav Engli 《Arkiv f?r Matematik》1992,30(1):227-243
In this paper it is shown that Toeplitz operators on Bergman space form a dense subset of the space of all bounded linear
operators, in the strong operator topology, and that their norm closure contains all compact operators. Further, theC
*-algebra generated by them does not contain all bounded operators, since all Toeplitz operators belong to the essential commutant
of certain shift. The result holds in Bergman spacesA
2(Ω) for a wide class of plane domains Ω⊂C, and in Fock spacesA
2(C
N),N≧1. 相似文献
20.
William Alexandre 《Mathematische Zeitschrift》2006,252(3):473-496
For a bounded convex domain with C∞ smooth boundary of finite type m and q=1, . . . ,n−1, we construct a -solving integral operator T*q such that for all k ∈ ℕ and the usual Ck and -norms the operator is continuous. 相似文献