共查询到20条相似文献,搜索用时 826 毫秒
1.
Thomas Schick 《Mathematische Nachrichten》2001,223(1):103-120
For non–compact manifolds with boundary we prove that bounded geometry defined by coordinate–free curvature bounds is equivalent to bounded geometry defined using bounds on the metric tensor in geodesic coordinates. We produce a nice atlas with subordinate partition of unity on manifolds with boundary of bounded geometry and we study the change of geodesic coordinate maps. 相似文献
2.
Sonia Mazzucchi Valter Moretti Ivan Remizov Oleg Smolyanov 《Mathematische Nachrichten》2023,296(3):1244-1284
Chernoff approximations of Feller semigroups and the associated diffusion processes in Riemannian manifolds are studied. The manifolds are assumed to be of bounded geometry, thus including all compact manifolds and also a wide range of non-compact manifolds. Sufficient conditions are established for a class of second order elliptic operators to generate a Feller semigroup on a (generally non-compact) manifold of bounded geometry. A construction of Chernoff approximations is presented for these Feller semigroups in terms of shift operators. This provides approximations of solutions to initial value problems for parabolic equations with variable coefficients on the manifold. It also yields weak convergence of a sequence of random walks on the manifolds to the diffusion processes associated with the elliptic generator. For parallelizable manifolds this result is applied in particular to the representation of Brownian motion on the manifolds as limits of the corresponding random walks. 相似文献
3.
We establish the equivalence between the family of uniformly regular Riemannian manifolds without boundary and the class of manifolds with bounded geometry. 相似文献
4.
Alexander Engel 《Journal of Functional Analysis》2019,276(7):2103-2155
We revisit ?pakula's uniform K-homology, construct the external product for it and use this to deduce homotopy invariance of uniform K-homology.We define uniform K-theory and on manifolds of bounded geometry we give an interpretation of it via vector bundles of bounded geometry. We further construct a cap product with uniform K-homology and prove Poincaré duality between uniform K-theory and uniform K-homology on spinc manifolds of bounded geometry. 相似文献
5.
We study fractional Sobolev and Besov spaces on noncompact Riemannian manifolds with bounded geometry. Usually, these spaces are defined via geodesic normal coordinates which, depending on the problem at hand, may often not be the best choice. We consider a more general definition subject to different local coordinates and give sufficient conditions on the corresponding coordinates resulting in equivalent norms. Our main application is the computation of traces on submanifolds with the help of Fermi coordinates. Our results also hold for corresponding spaces defined on vector bundles of bounded geometry and, moreover, can be generalized to Triebel‐Lizorkin spaces on manifolds, improving [11]. 相似文献
6.
We characterize functions which are growth types of Riemannian manifolds of bounded geometry. 相似文献
7.
This article examines statistical inverse problems on compact Riemannian manifolds. The approach is to use aspects of spectral
geometry associated with the Laplace-Beltrami operator on compact Riemannian manifolds. Optimality in terms of upper and lower
rates of convergence is established. It turns out that if the operator is polynomially bounded, then optimal convergence is
polynomial, while if the operator is exponentially bounded, then optimal convergence proceeds logarithmically. Application
to estimating the initial heat distribution is analyzed. 相似文献
8.
Mathematical Notes - The sub-Laplacian plays a key role in CR geometry. In this paper, we investigate eigenvalues of the sub-Laplacian on bounded domains of strictly pseudoconvex CR manifolds,... 相似文献
9.
We prove a Lipschitz-Volume rigidity theorem for the non-collapsed Gromov–Hausdorff limits of manifolds with Ricci curvature bounded from below. This is a counterpart of the Lipschitz-Volume rigidity in Alexandrov geometry. 相似文献
10.
We prove a general embedding theorem for Sobolev spaces on open manifolds of bounded geometry and infer from this the module structure theorem. Thereafter we apply this to weighted Sobolev spaces. 相似文献
11.
In this paper,we study the relation between the excess of open manifolds and their topology by using the methods of comparison geometry.We prove that a complete open Riemmannian manifold with Ricci curvature negatively lower bounded is of finite topological type provided that the conjugate radius is bounded from below by a positive constant and its Excess is bounded by some function of its conjugate radius,which improves some results in [4]. 相似文献
12.
Uniform Shapiro-Lopatinski Conditions and Boundary Value Problems on Manifolds with Bounded Geometry
Potential Analysis - We study the regularity of the solutions of second order boundary value problems on manifolds with boundary and bounded geometry. We first show that the regularity property of... 相似文献
13.
We prove that on open manifolds of bounded geometry satisfying a certain spectral condition the component of the identity D
infw,0
supr
of form preserving diffeomorphisms is a submanifold of the identity component of all bounded Sobolev diffeomorphisms. D
infw,0
supr
inherits a natural Riemannian geometry and we can solve Euler equations in this context.Research supported by NSF grant # DMS-9303215 and Emory-Greifswald Exchange Program 相似文献
14.
Jürgen Eichorn 《Journal of Mathematical Sciences》1999,94(2):1162-1176
A quite general theory of manifolds of maps between open manifolds of bounded geometry is constructed. The results of the
paper can be applied to the case of compact manifolds, but the method used differs from the traditional approach of Ebin and
Marsden. Bibliography: 11 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 234, 1996, pp. 41–65. 相似文献
15.
In this article, we study closed Riemannian manifolds with small excess. We show that a closed connected Riemannian manifold
with Ricci curvature and injectivity radius bounded from below is homeomorphic to a sphere if it has sufficiently small excess.
We also show that a closed connected Riemannian manifold with weakly bounded geometry is a homotopy sphere if its excess is
small enough. 相似文献
16.
We prove that simply connected open manifolds of bounded geometry, linear growth and sublinear filling growth (e.g. finite filling area) are simply connected at infinity. 相似文献
17.
Isaac Pesenson 《Journal of Geometric Analysis》2009,19(2):390-419
An approximation theory by bandlimited functions (≡ Paley-Wiener functions) on Riemannian manifolds of bounded geometry is
developed. Based on this theory multiscale approximations to smooth functions in Sobolev and Besov spaces on manifolds are
obtained. The results have immediate applications to the filtering, denoising and approximation and compression of functions
on manifolds. There exists applications to problems arising in data dimension reduction, image processing, computer graphics,
visualization and learning theory.
相似文献
18.
19.
Summary According to [CG4]|and [CFG], the complete manifolds with bounded sectional curvature and finite volume admit positive rank F-structures near infinity. In this paper, we show that, in dimension four, if the manifolds also have bounded covering geometry near infinity, then there exist F-structures with special topological properties. F-structures with these properties cannot be constructed solely by means of the general methods in [CG4]|and [CFG]. Using these special properties we prove a conjecture of Cheeger-Gromov on the rationality of the geometric signatures in the four dimensional case.Oblatum 15-XI-1993This work was partially supported by NSF Grant NSF DMS 9204095. 相似文献
20.
Ingolf Buttig 《Annals of Global Analysis and Geometry》1988,6(1):55-107
The author considers a discretization of the p-form Laplacian on open complete Riemannian manifolds of bounded geometry. Following Dodziuk and Patodi [8], the eigenvalues below the essential spectrum together with their eigenforms are approximated by eigenvalues and eigencochains of a semicombinatorical Laplacian acting on L
2-cochains. We obtain a similar result for a ray which is contained in the essential spectrum. An example of a manifold of bounded geometry which admits eigenvalues below the essential spectrum is constructed. 相似文献