Related papers: Local set approximation: Mattila-Vuorinen type set…

Let $K\subset\mathbb R^d$ be a compact subset equipped with a $\delta$-Ahlfors regular measure $\mu$. For any $\tau>1/d$ and any ``inhomogeneous'' vector $\boldsymbol{\theta}\in\mathbb R^d$, let $W_d(\psi_\tau,\boldsymbol{\theta})$ denote…

This paper focuses on investigating generalized relative interior notions for sets in locally convex topological vector spaces with particular attentions to graphs of set-valued mappings and epigraphs of extended-real-valued functions. We…

The knowledge of {\it non usual} and sometimes {\it hidden} symmetries of (classical) integrable systems provides a very powerful setting-out of solutions of these models. Primarily, the understanding and possibly the quantisation of…

Partially ordered sets (posets) play a universal role as an abstract structure in many areas of mathematics. For finite posets, an explicit enumeration of distinct partial orders on a set of unlabelled elements is known only up to a…

Let G be a connected split reductive group over a p-adic field. In the first part of the paper we prove, under certain assumptions on G and the prime p, a localization theorem of Beilinson-Bernstein type for admissible locally analytic…

In the present work, a theoretical framework focussing on local geometric deformations is introduced in order to cope with the problem of how to join spacetimes with different geometries and physical properties. Using this framework, it is…

We study differential $p$-forms on non-smooth and possibly fractal metric measure spaces, endowed with a local Dirichlet form. Using this local Dirichlet form, we prove a result on the localization of antisymmetric functions of $p+1$…

Local learning of sparse image models has proven to be very effective to solve inverse problems in many computer vision applications. To learn such models, the data samples are often clustered using the K-means algorithm with the Euclidean…

We present an index for the local sensitivity of spatiotemporal structures in coupled oscillatory systems based on the asymptotic scaling of local-in-space, finite-time Lyapunov Exponents. For a system of nonlocally-coupled R\"{o}ssler…

Measurable sets are defined as those locally approximable, in a certain sense, by sets in the given algebra (or ring). A corresponding measure extension theorem is proved. It is also shown that a set is locally approximable in the mentioned…

Surface integrals on density level sets often appear in asymptotic results in nonparametric level set estimation (such as for confidence regions and bandwidth selection). Also surface integrals can be used to describe the shape of level…

This paper unites the gauge-theoretic and hyperbolic-geometric perspectives on the asymptotic geometry of the character variety of SL(2,C) representations of a surface group. Specifically, we find an asymptotic correspondence between the…

In this paper, we consider a non-local approximation of the time-dependent Eikonal equation defined on a Riemannian manifold. We show that the local and the non-local problems are well-posed in the sense of viscosity solutions and we prove…

We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold. This extends the classical notion of asymptotic directions usually defined on smooth submanifolds. We…

Lattice discretizations of continuous manifolds are common tools used in a variety of physical contexts. Conventional discrete approximations, however, cannot capture all aspects of the original manifold, notably its topology. In this paper…

Local minimizers for the anisotropic isoperimetric problem in the small-volume regime on closed Riemannian manifolds are shown to be geodesically convex and small smooth perturbations of tangent Wulff shapes, quantitatively in terms of the…

For an m by n real matrix A, we investigate the set of badly approximable targets for A as a subset of the m-torus. It is well known that this set is large in the sense that it is dense and has full Hausdorff dimension. We investigate the…

The paper aims to initiate a systematic study of conformal mappings between Finsler spacetimes and, more generally, between pseudo-Finsler spaces. This is done by extending several results in pseudo-Riemannian geometry which are necessary…

We define the notion of asymptotically free for locally restricted compositions, which means roughly that large parts can often be replaced by any larger parts. Two well-known examples are Carlitz and alternating compositions. We show that…

In this paper we develop a general theory of metric Diophantine approximation for systems of linear forms. A new notion of `weak non-planarity' of manifolds and more generally measures on the space of $m\times n$ matrices over $\Bbb R$ is…