共查询到20条相似文献,搜索用时 46 毫秒
1.
E. Batzies 《Proceedings of the American Mathematical Society》2007,135(10):3341-3347
We establish a homeomorphism between the moduli space of ordered -tuples of 2-dimensional linear subspaces (mod ) and the quotient by simultaneous conjugation of a certain open subset . For , this leads to an explicit computation of the moduli space of central 2-arrangements in mod and its subspace of those classes that contain a complex hyperplane arrangement.
2.
Luis J. Alí as Abdê nago Barros Aldir Brasil Jr. 《Proceedings of the American Mathematical Society》2005,133(3):875-884
Let be a compact hypersurface with constant mean curvature immersed into the unit Euclidean sphere . In this paper we derive a sharp upper bound for the first eigenvalue of the stability operator of in terms of the mean curvature and the length of the total umbilicity tensor of the hypersurface. Moreover, we prove that this bound is achieved only for the so-called -tori in , with . This extends to the case of constant mean curvature hypersurfaces previous results given by Wu (1993) and Perdomo (2002) for minimal hypersurfaces.
3.
Petr Holicky Tamá s Keleti 《Proceedings of the American Mathematical Society》2005,133(6):1851-1859
It is known that the sets of extreme and exposed points of a convex Borel subset of are Borel. We show that for there exist convex subsets of such that the sets of their extreme and exposed points coincide and are of arbitrarily high Borel class. On the other hand, we show that the sets of extreme and of exposed points of a convex set of additive Borel class are of ambiguous Borel class . For proving the latter-mentioned results we show that the union of the open and the union of the closed segments of are of the additive Borel class if is a convex set of additive Borel class .
4.
Andrew G. Bakan 《Proceedings of the American Mathematical Society》2008,136(10):3579-3589
It has been proved that algebraic polynomials are dense in the space , , iff the measure is representable as with a finite non-negative Borel measure and an upper semi-continuous function such that is a dense subset of the space as equipped with the seminorm . The similar representation ( ) with the same and ( , and is also a dense
subset of ) corresponds to all those measures (supported by ) that are uniquely determined by their moments on ( ). The proof is based on de Branges' theorem (1959) on weighted polynomial approximation. A more general question on polynomial denseness in a separable Fréchet space in the sense of Banach has also been examined.
5.
Bassam Shayya 《Proceedings of the American Mathematical Society》2007,135(4):1107-1113
We prove that the Fourier transform of an function can be restricted to any compact convex surface of revolution in .
6.
Bernd Ammann Emmanuel Humbert Mohameden Ould Ahmedou 《Proceedings of the American Mathematical Society》2007,135(2):489-493
We prove a Pohozaev type identity for non-linear eigenvalue equations of the Dirac operator on Riemannian spin manifolds with boundary. As an application, we obtain that the mean curvature of a conformal immersion satisfies where is a conformal vector field on and where the integration is carried out with respect to the Euclidean volume measure of the image. This identity is analogous to the Kazdan-Warner obstruction that appears in the problem of prescribing the scalar curvature on inside the standard conformal class.
7.
Lucian Badescu 《Proceedings of the American Mathematical Society》2008,136(5):1505-1513
Let be a submanifold of dimension of the complex projective space . We prove results of the following type.i) If is irregular and , then the normal bundle is indecomposable. ii) If is irregular, and , then is not the direct sum of two vector bundles of rank . iii) If , and is decomposable, then the natural restriction map is an isomorphism (and, in particular, if is embedded Segre in , then is indecomposable). iv) Let and , and assume that is a direct sum of line bundles; if assume furthermore that is simply connected and is not divisible in . Then is a complete intersection. These results follow from Theorem 2.1 below together with Le Potier's vanishing theorem. The last statement also uses a criterion of Faltings for complete intersection. In the case when this fact was proved by M. Schneider in 1990 in a completely different way.
8.
N. Bejhaj Rhouma 《Proceedings of the American Mathematical Society》2003,131(12):3747-3755
We show the existence of principal eigenvalues of the problem in where is an indefinite weight function. The existence of a continuous family of principal eigenvalues is demonstrated. Also, we prove the existence of a principal eigenvalue for which the principal eigenfunction at .
9.
Pengzi Miao 《Proceedings of the American Mathematical Society》2004,132(1):217-222
We give a new construction of asymptotically flat and scalar flat metrics on with a stable minimal sphere. The existence of such a metric gives an affirmative answer to a question raised by R. Bartnik (1989).
10.
Boaz Tsaban 《Proceedings of the American Mathematical Society》2006,134(3):881-891
We construct several topological groups with very strong combinatorial properties. In particular, we give simple examples of subgroups of (thus strictly -bounded) which have the Menger and Hurewicz properties but are not -compact, and show that the product of two -bounded subgroups of may fail to be -bounded, even when they satisfy the stronger property . This solves a problem of Tkacenko and Hernandez, and extends independent solutions of Krawczyk and Michalewski and of Banakh, Nickolas, and Sanchis. We also construct separable metrizable groups of size continuum such that every countable Borel -cover of contains a -cover of .
11.
Richard L. Baker 《Proceedings of the American Mathematical Society》2004,132(9):2577-2591
Let be the set of real numbers, and define . We construct a complete measure space where the -algebra contains the Borel subsets of , and is a translation-invariant measure such that for any measurable rectangle , if , then , where is Lebesgue measure on . The measure is not -finite. We prove three Fubini theorems, namely, the Fubini theorem, the mean Fubini-Jensen theorem, and the pointwise Fubini-Jensen theorem. Finally, as an application of the measure , we construct, via selfadjoint operators on , a ``Schrödinger model' of the canonical commutation relations: , , .
12.
Xiaojiang Yu 《Proceedings of the American Mathematical Society》2006,134(2):491-499
We prove that for any real expansive matrix , there exists a bounded -dilation wavelet set in the frequency domain (the inverse Fourier transform of whose characteristic function is a band-limited single wavelet in the time domain ). Moreover these wavelet sets can approximate a cube in arbitrarily. This result improves Dai, Larson and Speegle's result about the existence of (basically unbounded) wavelet sets for real expansive matrices.
13.
We show that the -algebra associated to the tail-equivalence relation on a Bratteli diagram, according to a procedure recently introduced by the first-named author and A. Lopes, is isomorphic to the -algebra of the diagram. More generally we consider an approximately proper equivalence relation on a compact space for which the quotient maps are local homeomorphisms. We show that the algebra associated to under the above-mentioned procedure is isomorphic to the groupoid -algebra .
14.
Patrick J. Rabier 《Proceedings of the American Mathematical Society》2007,135(12):3875-3885
If is an system of differential operators on having continuous coefficients with vanishing oscillation at infinity, the Cordes-Illner theory ensures that is Fredholm from to for all or no value We prove that both the index (when defined) and the spectrum of are independent of
15.
W. K. Ziemer 《Proceedings of the American Mathematical Society》2004,132(7):1987-1995
It is shown that a -cell (the homeomorphic image of a closed ball in ) in , , cannot support a function in if [\frac{k+1}{2}]$">, the greatest integer in .
16.
Georgia Benkart Paul Terwilliger 《Proceedings of the American Mathematical Society》2007,135(6):1659-1668
We consider the three-point loop algebra, where denotes a field of characteristic 0 and is an indeterminate. The universal central extension of was determined by Bremner. In this note, we give a presentation for via generators and relations, which highlights a certain symmetry over the alternating group . To obtain our presentation of , we use the realization of as the tetrahedron Lie algebra.
17.
Wieslaw Pawlucki 《Proceedings of the American Mathematical Society》2005,133(2):481-484
For each positive integer we construct a -function of one real variable, the graph of which has the following property: there exists a real function on which is -extendable to , for each finite, but it is not -extendable.
18.
Michael A. Hill 《Proceedings of the American Mathematical Society》2007,135(12):4075-4086
In this paper, we introduce a Hopf algebra, developed by the author and André Henriques, which is usable in the computation of the -homology of a space. As an application, we compute the -homology of in a manner analogous to Mahowald and Milgram's computation of the -homology .
19.
Jan Kolá r Jan Kristensen 《Proceedings of the American Mathematical Society》2005,133(6):1699-1706
For a -smooth bump function we show that the gradient range is the closure of its interior, provided that admits a modulus of continuity satisfying as . The result is a consequence of a more general result about gradient ranges of bump functions of the same degree of smoothness. For such bump functions we show that for open sets , either the intersection is empty or its topological dimension is at least two. The proof relies on a new Morse-Sard type result where the smoothness hypothesis is independent of the dimension of the space.
20.
In this paper some upper bounds for the volume and diameter of central sections of symmetric convex bodies are obtained in terms of the isotropy constant of the polar body. The main consequence is that every symmetric convex body in of volume one has a proportional section , dim ( ), of diameter bounded by whenever the polar body is in isotropic position ( is some absolute constant).