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1.
Juan A. Aledo José M. Espinar José A. Gálvez 《Calculus of Variations and Partial Differential Equations》2007,29(3):347-363
We study isometric immersions of surfaces of constant curvature into the homogeneous spaces and . In particular, we prove that there exists a unique isometric immersion from the standard 2-sphere of constant curvature
c > 0 into and a unique one into when c > 1, up to isometries of the ambient space. Moreover, we show that the hyperbolic plane of constant curvature c < −1 cannot be isometrically immersed into or .
J.A. Aledo was partially supported by Ministerio de Education y Ciencia Grant No. MTM2004-02746 and Junta de Comunidades de
Castilla-La Mancha, grant no. PAI-05-034.
J.M. Espinar and J.A. Gálvez were partially supported by Ministerio de Education y Ciencia grant no. MTM2004-02746 and Junta
de Andalucía Grant No. FQM325. 相似文献
2.
We consider the sub-Riemannian metric g
h
on given by the restriction of the Riemannian metric of curvature 1 to the plane distribution orthogonal to the Hopf vector
field. We compute the geodesics associated to the Carnot–Carathéodory distance and we show that, depending on their curvature,
they are closed or dense subsets of a Clifford torus. We study area-stationary surfaces with or without a volume constraint
in (). By following the ideas and techniques by Ritoré and Rosales (Area-stationary surfaces in the Heisenberg group , arXiv:math.DG/0512547) we introduce a variational notion of mean curvature, characterize stationary surfaces, and prove
classification results for complete volume-preserving area-stationary surfaces with non-empty singular set. We also use the
behaviour of the Carnot–Carathéodory geodesics and the ruling property of constant mean curvature surfaces to show that the
only C
2 compact, connected, embedded surfaces in () with empty singular set and constant mean curvature H such that is an irrational number, are Clifford tori. Finally we describe which are the complete rotationally invariant surfaces with
constant mean curvature in ().
A. Hurtado has been partially supported by MCyT-Feder research project MTM2004-06015-C02-01.
C. Rosales has been supported by MCyT-Feder research project MTM2004-01387. 相似文献
3.
Luis J. Alías Marcos Dajczer Jaime Ripoll 《Annals of Global Analysis and Geometry》2007,31(4):363-373
The classical Bernstein theorem asserts that any complete minimal surface in Euclidean space
that can be written as the graph of a function on
must be a plane. In this paper, we extend Bernstein’s result to complete minimal surfaces in (may be non-complete) ambient
spaces of non-negative Ricci curvature carrying a Killing field. This is done under the assumption that the sign of the angle
function between a global Gauss map and the Killing field remains unchanged along the surface. In fact, our main result only
requires the presence of a homothetic Killing field.
L.J. Alías was partially supported by MEC/FEDER project MTM2004-04934-C04-02, F. Séneca project 00625/PI/04, and F. Séneca
grant 01798/EE/05, Spain 相似文献
4.
Nuria Corral 《Bulletin of the Brazilian Mathematical Society》2009,40(2):181-224
The polar curves of foliations having a curve C of separatrices generalize the classical polar curves associated to hamiltonian foliations of C. As in the classical theory, the equisingularity type ℘() of a generic polar curve depends on the analytical type of , and hence of C. In this paper we find the equisingularity types ε(C) of C, that we call kind singularities, such that ℘() is completely determined by ε(C) for Zariski-general foliations . Our proofs are mainly based on the adjunction properties of the polar curves. The foliation-like framework is necessary,
otherwise we do not get the right concept of general foliation in Zariski sense and, as we show by examples, the hamiltonian
case can be out of the set of general foliations.
The author was partially supported by the research projects MTM2007-66262 (Ministerio de Educación y Ciencia), MTM2006-15338-C02-02
(Ministerio de Educación y Ciencia),VA059A07 (Junta de Castilla y León) and PGIDITI06PXIB377128PR (Xunta de Galicia). 相似文献
5.
Daniel Girela José Ángel Peláez Fernando Pérez-González Jouni Rättyä 《Integral Equations and Operator Theory》2008,61(4):511-547
In this paper we study the positive Borel measures μ on the unit disc in for which the Bloch space is continuously included in , 0 < p < ∞. We call such measures p-Bloch-Carleson measures. We give two conditions on a measure μ in terms of certain logarithmic integrals one of which is a necessary condition and the other a sufficient condition for μ being a p-Bloch-Carleson measure. We also give a complete characterization of the p-Bloch-Carleson measures within certain special classes of measures. It is also shown that, for p > 1, the p-Bloch-Carleson measures are exactly those for which the Toeplitz operator , defined by , maps continuously into the Bergman space A
1, . Furthermore, we prove that if p > 1, α >-1 and ω is a weight which satisfies the Bekollé-Bonami -condition, then the measure defined by is a p-Bloch-Carleson-measure.
We also consider the Banach space of those functions f which are analytic in and satisfy , as . The Bloch space is contained in . We describe the p-Carleson measures for and study weighted composition operators and a class of integration operators acting in this space. We determine which of
these operators map continuously to the weighted Bergman space and show that they are automatically compact.
This research is partially supported by several grants from “the Ministerio de Educación y Ciencia, Spain” (MTM2005-07347,
MTM2007-60854, MTM2006-26627-E, MTM2007-30904-E and Ingenio Mathematica (i-MATH) No. CSD2006-00032); from “La Junta de Andalucía”
(FQM210 and P06-FQM01504); from “the Academy of Finland” (210245) and from the European Networking Programme “HCAA” of the
European Science Foundation. 相似文献
6.
7.
In this paper we have proved several approximation theorems for the family of minimal surfaces in that imply, among other things, that complete minimal surfaces are dense in the space of all minimal surfaces endowed with
the topology of C
k
convergence on compact sets, for any .
As a consequence of the above density result, we have been able to produce the first example of a complete proper minimal
surface in with uncountably many ends.
This research is partially supported by MEC-FEDER Grant no. MTM2004 - 00160. 相似文献
8.
Ruben Jakob 《Calculus of Variations and Partial Differential Equations》2007,28(3):383-409
In this paper we derive a sufficient condition for the existence of extremal surfaces of a parametric functional
with a dominant area term, which do not furnish global minima of
within the class
of H
1,2-surfaces spanning an arbitrary closed rectifiable Jordan curve
that merely has to satisfy a chord-arc condition. The proof is based on the “mountain pass result” of (Jakob in Calc Var 21:401–427, 2004) which yields an unstable
-extremal surface bounded by an arbitrary simple closed polygon and Heinz’ ”approximation method” in (Arch Rat Mech Anal 38:257–267,
1970). Hence, we give a precise proof of a partial result of the mountain pass theorem claimed by Shiffman in (Ann Math 45:543–576, 1944) who only outlined a very sketchy and partially incorrect proof. 相似文献
9.
María J. Carro 《Mathematische Zeitschrift》2007,255(4):813-825
Given a sublinear operator T such that is bounded, it can be shown that is bounded, with constant C/(1−q), for every 0 < q < 1. In this paper, we study the converse result, not only for sequence spaces, but for general measure spaces proving that,
if T : L
q
(μ) → X is bounded, with constant C/(1−q), for every and X is Banach, then T : L log (1/L)(μ) → X is bounded. Moreover, this result is optimal. We also show that things are quite different if the Banach condition on X is dropped.
This work has been partially supported by MTM2004-02299 and by 2005SGR00556. 相似文献
10.
Adrien Dubouloz 《Mathematische Zeitschrift》2007,255(1):77-93
Given complex algebraic varieties X and Y of the same dimension, the Cancellation Problem asks if an isomorphism between X ×
and Y ×
induces an isomorphism between X and Y. Iitaka and Fujita (J. Fac. Sci. Univ. 24:123–127, 1977) established that the answer is positive for a large class of varieties of any dimension. In 1989, Danielewski constructed a counterexample using smooth rational affine surfaces. His construction was further generalized by Fieseler (Comment. Math. Helvetici 69:5–27, 1994) and Wilkens (C.R. Acad. Sci. Paris Sér. I Math. 326(9):1111–1116, 1998) to describe a larger class of affine surfaces. Here we introduce higher-dimensional analogues of these surfaces. By studying algebraic actions of the additive group
on certain of these varieties, we obtain new counterexamples to the Cancellation Problem in every dimension d ≥ 2. 相似文献
11.
J. M. Calabuig F. Galaz-Fontes E. Jiménez-Fernández E. A. Sánchez Pérez 《Mathematische Zeitschrift》2007,257(2):381-402
In this paper, we characterize the space of multiplication operators from an L
p
-space into a space L
1(m) of integrable functions with respect to a vector measure m, as the subspace defined by the functions that have finite p-semivariation. We prove several results concerning the Banach lattice structure of such spaces. We obtain positive results—for
instance, they are always complete, and we provide counterexamples to prove that other properties are not satisfied—for example,
simple functions are not in general dense. We study the operators that factorize through , and we prove an optimal domain theorem for such operators. We use our characterization to generalize the Bennet–Maurey–Nahoum
Theorem on decomposition of functions that define an unconditionally convergent series in L
1[0,1] to the case of 2-concave Banach function spaces.
The research was partially supported by Proyecto MTM2005-08350-c03-03 and MTN2004-21420-E (J. M. Calabuig). Proyecto CONACyT
42227 (F. Galaz-Fontes). Proyecto MTM2006-11690-c02-01 and Feder (E. Jiménez-Fernández and E. A. Sánchez Pérez). 相似文献
12.
Laguerre geometry of surfaces in is given in the book of Blaschke [Vorlesungen über Differentialgeometrie, Springer, Berlin Heidelberg New York (1929)], and has been studied by Musso and Nicolodi [Trans. Am. Math. soc. 348, 4321–4337 (1996); Abh. Math. Sem. Univ. Hamburg 69, 123–138 (1999); Int. J. Math. 11(7), 911–924 (2000)], Palmer [Remarks on a variation problem in Laguerre geometry. Rendiconti di Mathematica, Serie VII, Roma, vol. 19, pp. 281–293 (1999)] and other authors. In this paper we study Laguerre differential geometry of hypersurfaces in . For any umbilical free hypersurface with non-zero principal curvatures we define a Laguerre invariant metric g on M and a Laguerre invariant self-adjoint operator : TM → TM, and show that is a complete Laguerre invariant system for hypersurfaces in with n≥ 4. We calculate the Euler–Lagrange equation for the Laguerre volume functional of Laguerre metric by using Laguerre invariants. Using the Euclidean space , the semi-Euclidean space and the degenerate space we define three Laguerre space forms , and and define the Laguerre embeddings and , analogously to what happens in the Moebius geometry where we have Moebius space forms S
n
, and (spaces of constant curvature) and conformal embeddings and [cf. Liu et al. in Tohoku Math. J. 53, 553–569 (2001) and Wang in Manuscr. Math. 96, 517–534 (1998)]. Using these Laguerre embeddings we can unify the Laguerre geometry of hypersurfaces in , and . As an example we show that minimal surfaces in or are Laguerre minimal in .C. Wang Partially supported by RFDP and Chuang-Xin-Qun-Ti of NSFC. 相似文献
13.
Alexander J. Zaslavski 《Calculus of Variations and Partial Differential Equations》2007,28(3):351-381
In this paper we study nonoccurrence of the Lavrentiev phenomenon for a large class of nonconvex nonautonomous constrained
variational problems. A state variable belongs to a convex subset of a Banach space with nonempty interior. Integrands belong
to a complete metric space of functions
which satisfy a growth condition common in the literature and are Lipschitzian on bounded sets. In our previous work Zaslavski
(Ann. Inst. H. Poincare, Anal. non lineare, 2006) we considered a class of nonconstrained variational problems with integrands
belonging to a subset
and showed that for any such integrand the infimum on the full admissible class is equal to the infimum on a subclass of
Lipschitzian functions with the same Lipschitzian constant. In the present paper we show that if an integrand f belongs to
, then this property also holds for any integrand which is contained in a certain neighborhood of f in
. Using this result we establish nonoccurrence of the Lavrentiev phenomenon for most elements of
in the sense of Baire category.
相似文献
14.
Luigi Ambrosio Estibalitz Durand-Cartagena 《Rendiconti del Circolo Matematico di Palermo》2009,58(1):1-10
This note is devoted to the differentiability properties of -Lipschitz maps defined on abstract Wiener spaces and with values in metric spaces (Y,d
Y
). We prove the existence γ-a.e. of local seminorms in the Cameron-Martin space which allow to compute the metric derivative of the map.
Second Author partially supported by DGES (Spain) MTM2006-03531. 相似文献
15.
Henri Heinich 《Journal of Theoretical Probability》2006,19(2):509-534
In this paper, we generalize the Kantorovich functional to K?the-spaces for a cost or a profit function. We examine the convergence
of probabilities with respect to this functional for some K?the-spaces. We study the Monge problem: Let
be a K?the-space, P and Q two Borel probabilities defined on a Polish space M and a cost function
. A K?the functional
is defined by
(P, Q) = inf
where
is the law of X. If c is a profit function, we note
. (P, Q) = sup
Under some conditions, we show the existence of a Monge function, φ, such that
, or
.
相似文献
16.
Humio Ichimura 《Archiv der Mathematik》2006,87(6):539-545
Let p be an odd prime number and
. Let
be the classical Stickelberger ideal of the group ring
. Iwasawa [6] proved that the index
equals the relative class number
of
. In [2], [4] we defined for each subgroup H of G a Stickelberger ideal
of
, and studied some of its properties. In this note, we prove that when
mod 4 and [G : H] = 2, the index
equals the quotient
.
Received: 13 January 2006 相似文献
17.
Bing Ye Wu 《Annals of Global Analysis and Geometry》2007,31(4):375-384
Let
be a Minkowski 3-space of Randers type with
, where
is the Euclidean metric and
. We consider minimal surfaces in
and prove that if a connected surface M in
is minimal with respect to both the Busemann–Hausdorff volume form and the Holmes–Thompson volume form, then up to a parallel
translation of
, M is either a piece of plane or a piece of helicoid which is generated by lines screwing about the x
3-axis.
相似文献
18.
Jean-Christophe Bourgoin 《Annals of Global Analysis and Geometry》2007,32(1):1-13
In this paper, we study the minimality of the map for the weighted energy functional , where is a continuous function. We prove that for any integer and any non-negative, non-decreasing continuous function f, the map minimizes E
f,p
among the maps in which coincide with on . The case p = 1 has been already studied in [Bourgoin J.-C. Calc. Var. (to appear)]. Then, we extend results of Hong (see Ann. Inst.
Poincaré Anal. Non-linéaire 17: 35–46 (2000)). Indeed, under the same assumptions for the function f, we prove that in dimension n ≥ 7 for any real with , the map minimizes E
f,p
among the maps in which coincide with on .
相似文献
19.
We consider a properly converging sequence of non-characters in the dual space of a thread-like group and investigate the limit set and the strength with which the sequence converges to each of its limits. We show that, if (π
k
) is a properly convergent sequence of non-characters in , then there is a trade-off between the number of limits σ which are not characters, their degrees, and the strength of convergence i
σ
to each of these limits (Theorem 3.2). This enables us to describe various possibilities for maximal limit sets consisting entirely of non-characters (Theorem 4.6). In Sect. 5, we show that if (π
k
) is a properly converging sequence of non-characters in and if the limit set contains a character then the intersection of the set of characters (which is homeomorphic to ) with the limit set has at most two components. In the case of two components, each is a half-plane. In Theorem 7.7, we show that if a sequence has a character as a cluster point then, by passing to a properly convergent subsequence and then a further subsequence, it is possible to find a real null sequence (c
k
) (with ) such that, for a in the Pedersen ideal of C
*(G
N
), exists (not identically zero) and is given by a sum of integrals over . 相似文献
20.
A maximal surface with isolated singularities in a complete flat Lorentzian 3-manifold
is said to be entire if it lifts to a (periodic) entire multigraph in . In addition, is called of finite type if it has finite topology, finitely many singular points and is a finitely sheeted multigraph. Complete (or proper) maximal immersions with isolated singularities in are entire, and entire embedded maximal surfaces in with a finite number of singularities are of finite type. We classify complete flat Lorentzian 3-manifolds carrying entire
maximal surfaces of finite type, and deal with the topology, Weierstrass representation and asymptotic behavior of this kind
of surfaces. Finally, we construct new examples of periodic entire embedded maximal surfaces in with fundamental piece having finitely many singularities.
相似文献