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1.
Let
be the unit disk of the complex plane. A conformai map of
into itself is called hyperbolically convex if the non-Euclidean segment between any two points of
also belongs to
. In this paper we prove several inequalities that are analogous to inequalities about (Euclidean) convex univalent functions.
We show that if ƒ (0) = 0, then Re zf′/f > 1/2. This inequality is the key for the results of this paper. In particular we
deduce a three-variable inequality corresponding to that of Ruscheweyh and Sheil-Small. The sharp bound for the Schwarzian
derivative remains open. 相似文献
2.
In this paper we investigate a class of Lie group actions on
, the so-calledpolar actions, that naturally generalize the standard
actions. For a domain invariant under such an action (i.e., a generalized Reinhardt domain) we characterize the invariant
plurisubharmonic functions and determine the envelope of holomorphy in geometric terms. For a generalized Reinhardt domain
containing the origin of
we also compute its automorphism group.
Supported in part by NSF Grant 8602020 相似文献
3.
The defect relation for holomorphic maps
in respect to slowly moving target hyperplanes in
is proved. The sharp defect boundn+1 is obtained.
Communicated by Yoram Sagher 相似文献
4.
E. Amar 《Journal of Geometric Analysis》1991,1(4):291-305
We show that if f1, f2 are bounded holomorphic functions in the unit ball
of ℂn such that
, |f1(z)|2 + |f2(z)2|2 ≥ δ2 >; 0, then any functionh in the Hardy space
,p < +∞ can be decomposed ash = f1h1
+ f2h2 with
. The Corona theorem in
would be the same result withp = +∞ and this question is still open forn ≳-2, but the preceding result goes in this direction. 相似文献
5.
Michael Christ 《Journal of Geometric Analysis》1991,1(3):193-230
For a large class of subharmonicφ, the equation
is studied in
. Pointwise upper bounds are derived for the distribution kernels of the canonical solution operator and of the orthogonal
projection onto the space of entire functions inH. Existence theorems inL
p norms are derived as a corollary. A class of counterexamples, related to the failure of
to be analytic-hypoelliptic on certain CR manifolds, is discussed.
Communicated by Steven Krantz 相似文献
6.
Given H≥0 and bounded convex curves α1, ...,⇌n, α in the plane z=0 bounding domains D1, …, Dn, D, respectively, with
if i ∈ j and with Di ⊂ D, we obtain several results proving the existence of a constanth depending only on H and on the geometry of the curves
αi, α such that the Dirichlet problem for the constant mean curvature H equation:
where
may accept or not a solution. 相似文献
7.
Existence of positive weak solutions with a prescribed singular set of semilinear elliptic equations
In this paper, we consider the problem of the existence of non-negative weak solution u of
having a given closed set S as its singular set. We prove that when
and S is a closed subset of Ω, then there are infinite many positive weak solutions with S as their singular set. Applying
this method to the conformal scalar curvature equation for n ≥ 9, we construct a weak solution
of
such that Sn is the singular set of u where L0 is the conformal Laplacian with respect to the standard metric of Sn. When n = 4 or 6, this kind of solution has been constructed by Pacard. 相似文献
8.
For any partial groupoid
, let Fr
be the free extension of
to a total groupoid. We show that
implies
and that the theory of Fr
is uniformly recursive in the theory of
. These results fail if “groupoid” is replaced by “semigroup”, “commutative semigroup”, “group”, “abelian group”, “semilattice”,
“K-lattice” for any nontrivial varietyK of lattices, or “Boolean algebra”.
Research supported in part by NSF Grant MCS78-01867. We thank the referee for his valuable comments.
Presented by B. Jónsson. 相似文献
9.
Lutz Strüngmann 《Israel Journal of Mathematics》2006,151(1):29-51
LetR be a unital associative ring and
two classes of leftR-modules. In [St3] the notion of a (
) pair was introduced. In analogy to classical cotorsion pairs, a pair (V,W) of subclasses
is called a (
) pair if it is maximal with respect to the classes
and the condition Ext
R
1
(V, W)=0 for all
. In this paper we study
pairs whereR = ℤ and
is the class of all torsion-free abelian groups andT is the class of all torsion abelian groups. A complete characterization is obtained assumingV=L. For example, it is shown that every
pair is singly cognerated underV=L.
The author was supported by a DFG grant. 相似文献
10.
M. B. Zvyagina 《Journal of Mathematical Sciences》1998,89(2):1122-1126
Let Λ be an associative ring with identity and let
be the category of left unitary Λ-modules. A subcateqory
of the category
is said to be small if the pairwise nonisomorphic objects of
form a set. The main result of this paper consists of the fact that for every small full subcategory
, there exists a ring Γ such that
is dual to a small full subcategory of the category
. Some applications of this result are indicated. Bibliography: 3 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 227, 1995, pp. 66–73. 相似文献
11.
Ignacio Bajo 《Monatshefte für Mathematik》1994,118(1-2):1-6
Let
be a complex Lie algebra,
its underlying real Lie algebra,
a real form of
and ·, · the euclidean product induced by the real part of an hermitian inner product on
. Let aut
be the Lie algebra of skew-symmetric derivations of
. We give necessary and sufficient conditions to ensure that aut
is composed of skew-hermitian derivations. As an application, we study holomorphy in large subgroups of isometries of Lie groups. 相似文献
12.
Karl-Hermann Neeb 《Semigroup Forum》1996,53(1):230-261
We say that an invariant convex coneW in a Lie algebras
is elliptic if its interior consists of elliptic elements of
. If such a cone exists, then
has a compactly embedded Cartan subalgebra. The first main result, of this paper is a characterization of those Lie algebras,
which contain elliptic invariant cones. If
is an invariant domain in such a cone, then we characterize the invariant locally convex functions onD by their restrictions to
where
is a compactly embedded Cartan subalgebra. 相似文献
13.
E. I. Timoshenko 《Algebra and Logic》1998,37(6):391-398
Part of any basis of a relatively free group
in the variety
is called a primitive system of elements. We provide a criterion of being primitive for
, where
is a variety of Abelian groups satisfying xm=1, and
a variety generated by a finite group. Let
be a variety of nilpotent groups of class ≤c. It is proved that, for the group
, the property of being primitive for an element g is stronger than the condition of being unimodular on a vector composed
of values of Fox derivatives in the ring
. The group
is not residually finite whenever a system of elements is primitive.
Supported by RFFR grant No. 96-01-01948.
Translated fromAlgebra i Logika, Vol. 37, No. 6, pp. 687–699, November–December, 1998. 相似文献
14.
Résumé Dans un célèbre papier ([3]), B. GIDAS et J.SPRUCK ont utilisé-sous des hypothèses adéquates- la technique du “blow up” pour
montrer que les solutionsu ∈C
0
∩C
1 (Ω) du problème
admettent une estimation a priori dansC
0
.
Dans ce travail, on montre que, si les solutionsu sont juste supposéesC
0
, une telle estimation a priori n’existe plus.
In a famous paper ([3]), B. GIDAS and J. SPRUCK used a “blow-up” argument to show that, under appropriate assumptions, all
the solutionsu ∈C
0
∩C
1 (Ω) of the problem
admit an a priori estimate inC
0
.
In this work, we show that, if one supposes the solutions are only inC
0
, such an a priori estimate does not hold. 相似文献
15.
16.
Andrew J. Sommese 《Milan Journal of Mathematics》1997,67(1):49-75
Let
be an algebraic submanifold of complex projective space ℙ
N
. Assume thatn:=dim
and let
denote the restriction of the hyperplane section bundle
to
. The meromorphic map
associated to
fork≥1 ties together the pluricanonical maps of the surface sections of
. Known results show that the behavior of
is far better than one would expect from experience with the pluricanonical mappings of algebraic surfaces. In this article
we discuss the known results on the structure of the mappings
and describe the open problems.
Conferenza tenuta il 5 giugno 1997 相似文献
17.
Götz Brunner 《Israel Journal of Mathematics》1972,12(3):306-313
In the definition ofCW-complexes, the one-point spaceP, respectively the spaceP∪* with basepoint *, play the roll of the only “building-stone”. Let
be a family of compact spaces. Then the definition of a generalizedCW-complex over
is obtained from the definition of aCW-complex by replacingP by the spaces of
and formation of the mapping cone by a slightly modified construction. LetCW
* denote the category of all pointed spaces which have the homotopy type of a generalizedCW-complex over
. If
, thenCW
* is the category of all pointedCW-spaces.CW
* is closed under the formation of direct sums and of mapping cones, cylinders and tori, and is formally characterized as
the smallest such subcategory of Top * containing the spaces W∪*,
. Following the methods of E. H. Brown, it is proved, that any half exact homotopy functor onCW
* is representable, and any cohomology theory onCW
is naturally equivalent to the cohomology theory of an Ω-spectrum; for example, the singular cohomo logy is representable
onCW
for any family
of compact spaces.
相似文献
18.
T. Levasseur 《Transformation Groups》1998,3(4):337-353
Let
u
be a compact Lie algebra and let
u
be its complexification. Let ζ−1/2 be the inverse on the set of regular elements of
u
of a square root of the discriminant of
. Generalizing a result of W. Lichtenstein in the case
u
=
(n, ℂ) or
(nℝ), we prove that ∂(q).ζ1/2 is non zero for all harmonic polynomialsq ∈S(
) \ {0}. This fact is deduced from results about equivariantD-modules supported on the nilpotent cone of
. 相似文献
19.
20.
This paper examines the following question. If
and
are saturated formations then
is defined to be the class of all soluble groups whose
belong to
. In general
is a formation, but need not be a saturated formation. Here the smallest saturated formation containing
is studied. 相似文献