1,720,959 research outputs found
q-parabolicity of stratified pseudomanifolds and other singular spaces
Full text linkThe main result of this paper is a sufficient condition to have a compact Thom–Mather stratified pseudomanifold endowed with a c^ -iterated edge metric on its regular part q-parabolic. Moreover, besides stratified pseudomanifolds, the q-parabolicity of other classes of singular spaces, such as compact complex Hermitian spaces, is investigated
Kac regular sets and Sobolev spaces in geometry, probability and quantum physics
Full text linkLet Ω ⊂ M be an open subset of a Riemannian manifold M and let V: M→ R be a Kato decomposable potential. With W01,2(M;V) the natural form domain of the Schrödinger operator - Δ + V in L2(M) , in this paper we study systematically the following question: Under which assumption on Ω is the statement for allf∈W01,2(M;V)withf=0a.e. inMΩone hasf|Ω∈W01,2(Ω;V)true for every such V? Generalizing a classical result by Herbst and Zhao, who treat the Euclidean Rm and V= 0 , we prove that without any further assumptions on V, the above property is satisfied, if Ω is Kac regular, a probabilistic property which means that the first exit time of Brownian motion on M from Ω is equal to its first penetration time to M Ω. In fact, we treat more general covariant Schrödinger operators acting on sections in metric vector bundles, allowing new results concerning the harmonicity of Dirac spinors on singular subsets. Finally, we prove that locally Lipschitz regular Ω ’s are Kac regular
Odd characteristic classes in entire cyclic homology and equivariant loop space homology
No full textGiven a compact manifoldM and a smooth map g:M → U.(l×l:C) from M to the Lie group of unitary l×l matrices with entries in C, we construct a Chern character Ch-(g) which lives in the odd part of the equivariant (entire) cyclic Chen-normalized cyclic complex Nε(ωT(M × T)) of M, and which is mapped to the odd Bismut-Chern character under the equivariant Chen integral map. It is also shown that the assignment g → Ch-(g) induces a well-defined group homomorphism from the K-1 theory of M to the odd homology group of Nε(ωT(M × T))
A Chern-Simons transgression formula for supersymmetric path integrals on spin manifolds
Full text linkEarlier results show that the N=1/2 supersymmetric path integral Jg on a closed even dimensional Riemannian spin manifold (X,g) can be constructed in a mathematically rigorous way via Chen differential forms and techniques from noncommutative geometry, if one considers Jg as a current on the loop space LX, that is, as a linear form on differential forms on LX. This construction admits a Duistermaat-Heckman localization formula. In this note, fixing a topological spin structure on X, we prove that any smooth family g•=(gt)t∈[0,1] of Riemannian metrics on X canonically induces a Chern-Simons current Cgjavax.xml.bind.JAXBElement@24e357bb which fits into a transgression formula for the supersymmetric path integral. In particular, this result entails that the supersymmetric path integral induces a differential topological invariant on X, which essentially stems from the Aˆ-genus of X
Neumann Cut-Offs and Essential Self-adjointness on Complete Riemannian Manifolds with Boundary
Full text linkWe generalize some fundamental results for noncompact Riemannian manfolds without boundary, that only require completeness and no curvature assumptions, to manifolds with boundary: let M be a smooth Riemannian manifold with boundary partial derivative M and let C-c(infinity)(M) denote the space of smooth compactly supported cut-off functions with vanishing normal derivative, Neumann cut-offs. We show, among other things, that under completeness: - C-c(infinity)(M) is dense in W1,p(M & ring;) for all p is an element of(1,infinity); this generalizes a classical result by Aubin [2] for partial derivative M=& empty;. - M admits a sequence of first order cut-off functions in C-c(infinity)(M); for partial derivative M=& empty; this result can be traced back to Gaffney [7]. - the Laplace-Beltrami operator with domain of definition C-c(infinity)(M) is essentially self-adjoint; this is a generalization of a classical result by Strichartz [20] for partial derivative M=& empty;
Scattering theory of the Hodge-Laplacian under a conformal perturbation
Full text linkLet g and g be Riemannian metrics on a noncompact manifold M, which are conformally equivalent. We show that under a very mild first order control on the conformal factor, the wave operators corresponding to the Hodge-Laplacians Δg and Δg acting on differential forms exist and are complete. We apply this result to Riemannian manifolds with bounded geometry and more specifically, to warped product Riemannian manifolds with bounded geometry. Finally, we combine our results with some explicit calculations by Antoci to determine the absolutely continuous spectrum of the Hodge-Laplacian on j-forms for a large class of warped product metrics
L^1-elliptic regularity and H = W on the whole L^p-scale on arbitrary manifolds
No full textWe define abstract Sobolev type spaces on Lp-scales, p ∈ [1,∞), on Hermitian vector bundles over possibly noncompact manifolds, which are induced by smooth measures and families B of linear partial differential operators, and we prove the density of the corresponding smooth Sobolev sections in these spaces under a generalised ellipticity condition on the underlying family. In particular, this implies a covariant version of Meyers-Serrin's theorem on the whole Lp-scale, for arbitrary Riemannian manifolds. Furthermore, we prove a new local elliptic regularity result in L1 on the Besov scale, which shows that the above generalised ellipticity condition is satisfied on the whole Lp-scale, if some differential operator from B that has a sufficiently high (but not necessarily the highest) order is elliptic
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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