Related papers: The weak convergence of varifolds generated by rec…

We prove under suitable hypotheses that convergence of integral varifolds implies convergence of associated mod 2 flat chains and subsequential convergence of associated integer-multiplicity rectifiable currents. The convergence results…

We prove (without using Federer's structure theorem) that a finite-mass flat chain over any coefficient group is rectifiable if and only if almost all of its 0-dimensional slices are rectifiable. This implies that every flat chain of finite…

We study the action on currents and differential forms on compact Riemannian manifolds under $C^0$-limits of diffeomorphisms. Using tools from geometric analysis, measure theory, and homotopy theory, we establish several convergence…

Several recent papers investigated unbounded versions of order and norm convergences in Banach lattices. In this paper, we study the unbounded variant of weak convergence and its relationship with other convergences. In particular, we…

It is shown that a simple closed curve in $\mathbb C^n$ that is a uniform limit of rectifiable simple closed curves each of which has nontrivial polynomial hull has itself nontrivial polynomial hull. In case the limit curve is rectifiable,…

Let h : R $\rightarrow$ R+ be a lower semi-continuous subbadditive and even function such that h(0) = 0 and h($\theta$) $\ge$ $\alpha$|$\theta$| for some $\alpha$ > 0. The h-mass of a k-polyhedral chain P =$\sum$j $\theta$j$\sigma$j in R n…

We consider a variational problem modeling transition between flat and wrinkled region in a thin elastic sheet, and identify the $\Gamma$-limit as the sheet thickness goes to 0, thus extending the previous work of the first author [Bella,…

We have derived that on certain Banach spaces having a graph structure $G$, the iterations for asymptotically $G$-nonexpansive map will converge weakly towards a fixed point. This result unifies and extends several theorems on fixed points…

In the short note, we describe a sampling construction that yields a sequence of graphons converging to a prescribed limit graphon in 1-norm. This convergence is stronger than the convergence in the cut norm, usually used to study graphon…

We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When…

A new approach to prove weak convergence of random polytopes on the space of compact convex sets is presented. This is used to show that the profile of the rescaled Schl\"afli random cone of a random conical tessellation generated by $n$…

We prove that for any weakly convergent sequence of finite graphs with bounded vertex degrees, there exists a topological limit graphing.

We prove that the range of sequence of vector measures converging widely satisfies a weak lower semicontinuity property, that the convergence of the range implies the strict convergence (convergence of the total variation) and that the…

Using the game approach to fragmentability, we give new and simpler proofs of the following known results: (a) If the Banach space admits an equivalent Kadec norm, then its weak topology is fragmented by a metric which is stronger than the…

Weak topologies that yield weak convergence for bounded sequences and nets in CAT($0$) spaces have been studied in the past. We are here concerned with weak topologies that yield weak convergence of unbounded sequences and nets. We analyze…

In this paper we define the closure under weak convergence of the class of p-tempered {\alpha}-stable distributions. We give necessary and sufficient conditions for convergence of sequences in this class. Moreover, we show that any element…

We introduce "weakly chained spaces", which need not be locally connected or path connected, but for which one has a reasonable notion of generalized fundamental group and associated generalized universal cover. We show that in the compact…

We give a criterion for H-convergence of conductivity matrices in terms of ordinary weak convergence of the factors in certain quotient representations of the matrices.

We prove that every flat chain with finite mass in $\mathbb{R}^d$ with coefficients in a normed abelian group $G$ is the restriction of a normal $G$-current to a Borel set. We deduce a characterization of real flat chains with finite mass…

This expository note aims at illustrating weak convergence of probability measures from a broader view than a previously published paper. Though the results are standard for functional analysts, this approach is rarely known by…