Related papers: Rough Paths on Manifolds
In this note we discuss the fundamental groups and diameters of positively Ricci curved $n$-manifolds. We use a method combining the results about equivarient Hausdorff convergence developed by Fukaya and Yamaguchi with the Ricci version of…
In this paper, we introduce and develop the concept of \emph{ramification} in a given modulus. We study some properties in relation to this concept and it's connection to some important problems in mathematics, particularly the Goldbach…
The paper is devoted to Hardy type inequalities on closed manifolds. By means of various weighted Ricci curvatures, we establish several sharp Hardy type inequalities on closed weighted Riemannian manifolds. Our results complement in…
We study the validity of an extension of Frobenius theorem on integral manifolds for some classes of Pfaff-type systems of partial differential equations involving multidimensional "rough" signals, i.e. "differentials" of given H\"older…
We show in this note how the machinery of C^1-approximate flows devised in the work "Flows driven by rough paths", and applied there to reprove and extend most of the results on Banach space-valued rough differential equations driven by a…
We construct a procedure for Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ) renormalization of a rough path in view of the relation between rough path theory and regularity structure. We also provide a plain expression of the BPHZ-renormalized…
We survey what is known about various special types of submanifolds of contact manifolds and discuss their role in the development of contact geometry.
This paper establishes the existence and uniqueness of solutions for rough differential equations driven by reduced rough paths with low regularity, specifically in the roughness regime $\frac{1}{3} < \alpha \leq \frac{1}{2}$. While the…
We consider submanifolds into Riemannian manifold with metallic structures. We obtain some new results for hypersurfaces in these spaces and we express the fundamental theorem of submanifolds into products spaces in terms of metallic…
We extend the recently developed rough path theory for Volterra equations from (Harang and Tindel, 2019) to the case of more rough noise and/or more singular Volterra kernels. It was already observed in (Harang and Tindel, 2019) that the…
In this article, we study questions pertaining to ramified $\mathbb{Z}_p^d$-extensions of a finite connected graph $X$. We also study the Iwasawa theory of dual graphs.
Calculus via regularizations and rough paths are two methods to approach stochastic integration and calculus close to pathwise calculus. The origin of rough paths theory is purely deterministic, calculus via regularization is based on…
In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.
We embed the geometries of the generalized $\lambda$-deformations into the framework of the Double Field Theory.
We study the existence of geometrically controlled branched covering maps from $\mathbb R^3$ to open $3$-manifolds or to decomposition spaces $\mathbb S^3/G$, and from $\mathbb S^3/G$ to $\mathbb S^3$.
In the present paper, we study several complex manifolds by using the following idea. First, we construct a certain moduli space and study the fundamental group of this space. This fundamental group is naturally mapped to the groups…
Given a non-compact Riemannian manifold M and a submanifold N of codimension q, we will construct under certain assumptions on both M and N a wrong way map in uniformly finite homology. Using an equivariant version of the construction and…
The universal limit theorem is a central result in rough path theory, which has been proved for: (i) rough paths with roughness $\frac{1}{3}< \alpha \leq \frac{1}{2}$; (ii) geometric rough paths with roughness $0< \alpha \leq 1$; (iii)…
We investigate the geometric implications of spectral curvature bounds, extending classical rigidity results in scalar curvature geometry to the spectral setting. By systematically employing the warped $\mu$-bubble method, we show…
A path-integral approach to non-perturbative topological invariants of knots, links and manifolds of dimension three and four using topological quantum field theory of Schwarz (Chern-Simons) type is presented.