共查询到20条相似文献,搜索用时 15 毫秒
1.
Ursula Ludwig 《Comptes Rendus Mathematique》2012,350(9-10):525-528
The aim of this Note is twofold. In the first step we study the Witten deformation for stratified spaces X and radial Morse functions on them and prove a spectral gap theorem for the Witten Laplacian. In the second step we focus on spaces with isolated conic singularities, where we construct a geometric complex associated to the Morse function and give two comparison results. 相似文献
2.
In this paper, we introduce weighted p-Sobolev spaces on manifolds with edge singularities. We give the proof for the corresponding edge type Sobolev inequality, Poincaré inequality and Hardy inequality. As an application of these inequalities, we prove the existence of nontrivial weak solutions for the Dirichlet problem of semilinear elliptic equations with singular potentials on manifolds with edge singularities. 相似文献
3.
Let X be an abstract compact orientable CR manifold of dimension ${2n-1, n\,\geqslant\,2}$ , and let L k be the k-th tensor power of a CR complex line bundle L over X. We assume that condition Y(q) holds at each point of X. In this paper we obtain a scaling upper-bound for the Szegö kernel on (0, q)-forms with values in L k , for large k. After integration, this gives weak Morse inequalities, analogues of the holomorphic Morse inequalities of Demailly. By a refined spectral analysis we obtain also strong Morse inequalities. We apply the strong Morse inequalities to the embedding of some convex–concave manifolds. 相似文献
4.
5.
Ursula Ludwig 《Comptes Rendus Mathematique》2009,347(13-14):801-804
In a previous Note the author gave a generalisation of Witten's proof of the Morse inequalities to the model of a singular complex algebraic curve X and a stratified Morse function f. In this Note a geometric interpretation of the complex of eigenforms of the Witten Laplacian corresponding to small eigenvalues is provided in terms of an appropriate subcomplex of the complex of unstable cells of critical points of f. To cite this article: U. Ludwig, C. R. Acad. Sci. Paris, Ser. I 347 (2009). 相似文献
6.
Misha Gromov 《Central European Journal of Mathematics》2014,12(7):923-951
We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all ?∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f. We show, for instance, that if X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurface of finite volume. 相似文献
7.
José Ángel Peláez 《Journal of Functional Analysis》2008,255(6):1403-1418
If X⊂Y are two classes of analytic functions in the unit disk D and θ is an inner function, θ is said to be (X,Y)-improving, if every function f∈X satisfying fθ∈Y must actually satisfy fθ∈X. This notion has been recently introduced by K.M. Dyakonov. In this paper we study the (X,Y)-improving inner functions for several pairs of spaces (X,Y). In particular, we prove that for any p∈(0,1) the (Qp,BMOA)-improving inner functions and the (Qp,B)-improving inner functions are precisely the inner functions which belong to the space Qp. Here, B is the Bloch space. We also improve some results of Dyakonov on the subject regarding Lipschitz spaces and Besov spaces. 相似文献
8.
Romain Tessera 《Geometriae Dedicata》2008,136(1):203-220
We introduce a quantitative version of Property A in order to estimate the L
p
-compressions of a metric measure space X. We obtain various estimates for spaces with sub-exponential volume growth. This quantitative property A also appears to
be useful to yield upper bounds on the L
p
-distortion of finite metric spaces. Namely, we obtain new optimal results for finite subsets of homogeneous Riemannian manifolds.
We also introduce a general form of Poincaré inequalities that provide constraints on compressions, and lower bounds on distortion.
These inequalities are used to prove the optimality of some of our results.
相似文献
9.
Wang Tixiang 《数学学报(英文版)》1989,5(3):250-262
LetM be aC
2-Finsler manifold modeled on a Banach space, and letf be aC
2-real-valued function defined onM. Using theA-gradient vector field which was introduced in [31] we give a suitable definition for nondegenegacy of critical points off, then generalize the Morse handle-body decomposition theorem and the Morse inequalities to a kind of Banach manifolds. A generalization in the reflexive case has been done in [31]. 相似文献
10.
We obtain new embedding theorems for Lorentz spaces of vector-valued martingales, thus generalizing the classical martingale
inequalities. In contrast to earlier methods, we use martingale transformations defined by sequences of operators and identify
the operator S
(p)(f) for a martingale f ranging in a Banach space X with the maximal operator for some ℓ
p
(X)-valued martingale transform. The obtained inequalities are closely related to geometric properties of the Banach space in
question. 相似文献
11.
Diego Chamorro 《Journal of Mathematical Analysis and Applications》2011,377(2):695-709
We study in this article the improved Sobolev inequalities with Muckenhoupt weights within the framework of stratified Lie groups. This family of inequalities estimate the Lq norm of a function by the geometric mean of two norms corresponding to Sobolev spaces and Besov spaces . When the value p which characterizes Sobolev space is strictly larger than 1, the required result is well known in Rn and is classically obtained by a Littlewood-Paley dyadic blocks manipulation. For these inequalities we will develop here another totally different technique. When p=1, these two techniques are not available anymore and following M. Ledoux (2003) [12], in Rn, we will treat here the critical case p=1 for general stratified Lie groups in a weighted functional space setting. Finally, we will go a step further with a new generalization of improved Sobolev inequalities using weak-type Sobolev spaces. 相似文献
12.
Let X be a compact connected CR manifold of dimension \(2n-1, n\ge 2\) with a transversal CR \(S^1\)-action on X. We study the Fourier components of the Kohn–Rossi cohomology with respect to the \(S^1\)-action. By studying the Szegö kernel of the Fourier components we establish the Morse inequalities on X. Using the Morse inequalities we have established on X we prove that there are abundant CR functions on X when X is weakly pseudoconvex and strongly pseudoconvex at a point. 相似文献
13.
This paper is devoted to the approximation of differentiable semialgebraic functions by Nash functions. Approximation by Nash functions is known for semialgebraic functions defined on an affine Nash manifold M, and here we extend it to functions defined on Nash sets X⊂Mwhose singularities are monomial. To that end we discuss first finiteness and weak normality for such sets X. Namely, we prove that (i) X is the union of finitely many open subsets, each Nash diffeomorphic to a finite union of coordinate linear varieties of an affine space, and (ii) every function on X which is Nash on every irreducible component of X extends to a Nash function on M. Then we can obtain approximation for semialgebraic functions and even for certain semialgebraic maps on Nash sets with monomial singularities. As a nice consequence we show that m-dimensional affine Nash manifolds with divisorial corners which are class k semialgebraically diffeomorphic, for k>m2, are also Nash diffeomorphic. 相似文献
14.
Misha Gromov 《Central European Journal of Mathematics》2014,12(8):1109-1156
Groping our way toward a theory of singular spaces with positive scalar curvatures we look at the Dirac operator and a generalized Plateau problem in Riemannian manifolds with corners. Using these, we prove that the set of C 2-smooth Riemannian metrics g on a smooth manifold X, such that scal g (x) ≥ κ(x), is closed under C 0-limits of Riemannian metrics for all continuous functions κ on X. Apart from that our progress is limited but we formulate many conjectures. All along, we emphasize geometry, rather than topology of manifolds with their scalar curvatures bounded from below. 相似文献
15.
Some atomic decomposition theorems are proved in vector-valued weak martingale Hardy spaces w
p
Σα(X), w
p
Q
α(X) and wD
α(X). As applications of atomic decompositions, a sufficient condition for sublinear operators defined on some vector-valued
weak martingale Hardy spaces to be bounded is given. In particular, some weak versions of martingale inequalities for the
operators f*, S
(p)(f) and σ(p)(f) are obtained.
This research was supported by the National Science Foundation of China (No. 10371093). 相似文献
16.
Let L be a non-negative self-adjoint operator acting on L2(X) where X is a space of homogeneous type. Assume that L generates a holomorphic semigroup e−tL whose kernels pt(x,y) have Gaussian upper bounds but there is no assumption on the regularity in variables x and y. In this article, we study weighted Lp-norm inequalities for spectral multipliers of L. We show that sharp weighted Hörmander-type spectral multiplier theorems follow from Gaussian heat kernel bounds and appropriate L2 estimates of the kernels of the spectral multipliers. These results are applicable to spectral multipliers for large classes of operators including Laplace operators acting on Lie groups of polynomial growth or irregular non-doubling domains of Euclidean spaces, elliptic operators on compact manifolds and Schrödinger operators with non-negative potentials. 相似文献
17.
Alessandro Berarducci Dikran Dikranjan Jan Pelant 《Topology and its Applications》2006,153(17):3355-3371
A metric space X is straight if for each finite cover of X by closed sets, and for each real valued function f on X, if f is uniformly continuous on each set of the cover, then f is uniformly continuous on the whole of X. The straight spaces have been studied in [A. Berarducci, D. Dikranjan, J. Pelant, An additivity theorem for uniformly continuous functions, Topology and its Applications 146-147 (2005) 339-352], which contains characterization of the straight spaces within the class of the locally connected spaces (they are the uniformly locally connected ones) and the class of the totally disconnected spaces (they coincide with the totally disconnected Atsuji spaces). We show that the completion of a straight space is straight and we characterize the dense straight subspaces of a straight space. In order to clarify further the relation between straightness and the level of local connectedness of the space we introduce two more intermediate properties between straightness and uniform local connectedness and we give various examples to distinguish them. One of these properties coincides with straightness for complete spaces and provides in this way a useful characterization of complete straight spaces in terms of the behaviour of the quasi-components of the space. 相似文献
18.
Let (??,??) be an infinite graph endowed with a reversible Markov kernel p and let P be the corresponding operator. We also consider the associated discrete gradient ?. We assume that ?? is doubling, a uniform lower bound for p(x,y) when p(x,y)>0, and gaussian upper estimates for the iterates of p. Under these conditions (and in some cases assuming further some Poincaré inequality) we study the comparability of (I?P)1/2 f and ?f in Lebesgue spaces with Muckenhoupt weights. Also, we establish weighted norm inequalities for a Littlewood?CPaley?CStein square function, its formal adjoint, and commutators of the Riesz transform with bounded mean oscillation functions. 相似文献
19.
S. V. Astashkin 《Functional Analysis and Its Applications》2013,47(2):148-151
We show that, for a broad class of symmetric spaces on [0, 1], the complementability of the subspace generated by independent functions f k (k = 1, 2,…) is equivalent to the complementability of the subspace generated by the disjoint translates $\bar f_k (t) = f_k (t - k + 1)\chi _{[k - 1,k]} (t)$ of these functions in some symmetric space Z X 2 on the semiaxis [0,∞). Moreover, if Σ k=1 ∞ m(supp f k ) ? 1, then Z X 2 can be replaced by X itself. This result is new even in the case of L p -spaces. A series of consequences is obtained; in particular, for the class of symmetric spaces, a result similar to a well-known theorem of Dor and Starbird on the complementability in L p [0, 1] (1 ? p < ∞) of the subspace [f k ] generated by independent functions provided that it is isomorphic to the space l p is obtained. 相似文献
20.
David Spring 《Topology and its Applications》1984,18(1):89-94
For reasonable spaces (including topological manifolds) X, Y, we characterize compact subsets of the space of continuous maps from X to Y, topologized with the fine (Whitney) C0-topology. In the case of smooth manifolds, we characterize also compact subsets of the space of Cr maps in the Whitney Cr topology. 相似文献