Related papers: Stokes' theorem for nonsmooth chains

We prove that a Riemannian submersion between smooth, compact, non-negatively curved Riemannian manifolds has to be smooth, resolving a conjecture by Berestovskii--Guijarro. We show that without any curvature assumption, the smoothness of…

For a smooth function on a smooth manifold of a suitable class, the space of all connected components of preimages is the graph and called the {\it Reeb graph}. Reeb graphs are fundamental tools in the algebraic and differential topological…

We provide a mathematical realization of a conjecture by Kitaev, on the basis of the operator-algebraic formulation of infinite quantum spin systems. Our main results are threefold. First, we construct an $\Omega$-spectrum $\mathit{IP}_*$…

Let $\Omega \subset \mathbb{C}^n$ be a domain whose Bergman space contains all holomorphic monomials. We derive sufficient conditions for $\Omega$ to be Reinhardt, complete Reinhardt, circular or Hartogs in terms of the orthogonality…

The theory of analytic function spaces in very general tubular domains over symmetric cones is a relatively new interesting research area. Tube domains are very general and very complicated domains. Recently several new results in this…

In this paper, we introduce the notion of a $\gamma$-density point for Lebesgue-measurable subsets of $\mathbb{R}$, where $\gamma$ is a modulus function, and study its basic measure-theoretic properties. We show that every $\gamma$-density…

Let $\omega$ be a closed, non-degenerate differential form of arbitrary degree. Associated to it there are an $L_{\infty}$-algebra of observables, and an $L_{\infty}$-algebra of sections of the higher Courant algebroid twisted by $\omega$.…

The paper deals with the problem of integration of equations of motion in nonholonomic systems. By means of well-known theory of the differential equations with an invariant measure the new integrable systems are discovered. Among them…

This paper presents a point-free version of the Lebesgue integral for simple functions on $\sigma$-locales. It describes the integral with respect to a measure defined on the coframe of all $\sigma$-sublocales, moving beyond the constraints…

In this paper we show that every $L^1$-integrable function on $\partial\Omega$ can be obtained as the trace of a function of bounded variation in $\Omega$ whenever $\Omega$ is a domain with regular boundary $\partial\Omega$ in a doubling…

We study nuclear embeddings for function spaces of generalised smoothness defined on a bounded Lipschitz domain $\Omega\subset\mathbb{R}^d$. This covers, in particular, the well-known situation for spaces of Besov and Triebel-Lizorkin…

In this article, we propose a general theory of integration of the Riemann and Lebesgue types with respect to arbitrary measures and functions, connected by a continuous bilinear product, with values in abstract vector spaces endowed with a…

We prove that an open set $\Omega \subset \mathbb{R}^n$ can be approximated by smooth sets of uniformly bounded perimeter from the interior if and only if the open set $\Omega$ satisfies \begin{align*} &\qquad…

A property of smooth convex domains $\Omega \subset \mathbb{R}^n$ is that if two points on the boundary $x, y \in \partial \Omega$ are close to each other, then their normal vectors $n(x), n(y)$ point roughly in the same direction and this…

This work is devoted to prove an optimum version of the trace inequality associated to the embedding $BV(\Omega)\subset L^1(\partial\Omega)$. Special emphasis is placed on the regularity that the domain $\Omega$ should exhibit for this…

In this paper we establish Gehring-Hayman type theorems for some complex domains. Suppose that $\Omega\subset \mathbb{C}^n$ is a bounded $m$-convex domain with Dini-smooth boundary, or a bounded strongly pseudoconvex domain with…

We leverage path differentiability and a recent result on nonsmooth implicit differentiation calculus to give sufficient conditions ensuring that the solution to a monotone inclusion problem will be path differentiable, with formulas for…

The purpose of this note is to prove a version of the Trace Theorem for domains which are locally subgraph of a H\" older continuous function. More precisely, let $\eta\in C^{0,\alpha}(\omega)$, $0<\alpha<1$ and let $\Omega_{\eta}$ be a…

We develop a general framework for pathwise stochastic integration that extends F\"ollmer's classical approach beyond gradient-type integrands and standard left-point Riemann sums and provides pathwise counterparts of It\^o, Stratonovich,…

This paper is concerned with extensions of geometric stability theory to some nonelementary classes. We prove the following theorem: Theorem: Let C be a large homogeneous model of a stable diagram D. Let p, q in S_D(A), where p is…