Recently, T. Fukui and L. Paunescu introduced a weighted version of the -regularity condition and Kuo’s ratio test condition. In this approach, we consider the - regularity condition and -regularity related to a Newton filtration.
Teardrops are generalizations of open mapping cylinders. We prove that the teardrop of a stratified approximate fibration X → Y × ℝ with X and Y homotopically stratified spaces is itself a homotopically stratified space (under mild hypothesis). This is applied to manifold stratified approximate fibrations between manifold stratified spaces in order to establish the realization part of a previously announced tubular neighborhood theory.
In this paper we introduce the sheaf of stratified Whitney jets of Gevrey order on the subanalytic site relative to a real analytic manifold . Then, we define stratified ultradistributions of Beurling and Roumieu type on . In the end, by means of stratified ultradistributions, we define tempered-stratified ultradistributions and we prove two results. First, if is a real surface, the tempered-stratified ultradistributions define a sheaf on the subanalytic site relative to . Second, the tempered-stratified...
, that is to say, Lorentzian manifolds with vanishing second derivative of the curvature tensor , are characterized by several geometric properties, and explicitly presented. Locally, they are a product where each factor is uniquely determined as follows: is a Riemannian symmetric space and is either a constant-curvature Lorentzian space or a definite type of plane wave generalizing the Cahen–Wallach family. In the proper case (i.e., at some point), the curvature tensor turns out to...
We study sub-Riemannian (Carnot-Caratheodory) metrics defined by noninvolutive distributions on real-analytic Riemannian manifolds. We establish a connection between regularity properties of these metrics and the lack of length minimizing abnormal geodesics. Utilizing the results of the previous study of abnormal length minimizers accomplished by the authors in [Annales IHP. Analyse nonlinéaire 13, p. 635-690] we describe in this paper two classes of the germs of distributions (called 2-generating...
The classical Wilson loop is the gauge-invariant trace of the parallel transport around a closed path with respect to a connection on a vector bundle over a smooth manifold. We build a precise mathematical model of the super Wilson loop, an extension introduced by Mason-Skinner and Caron-Huot, by endowing the objects occurring with auxiliary Graßmann generators coming from -points. A key feature of our model is a supergeometric parallel transport, which allows for a natural notion of holonomy on...