Related papers: A Newman property for BLD-mappings

We prove a characterization for BLD-mappings between locally complete locally compact path-metric spaces. As a corollary we obtain a sharp limit theorem for BLD-mappings.

We give a proof, based on Lipschitz quotient mappings, for the fact that limits of BLD-mappings between manifolds of bounded geometry are BLD. Furthermore we show that such mappings share some properties of covering maps and especially have…

In this paper, we present a new characterization of the mappings of bounded length distortion (BLD for short). In the original geometric definition it is assumed that a BLD mapping is open, discrete and sense preserving. We prove that the…

A Laplacian eigenfunction on a two-dimensional manifold dictates some natural partitions of the manifold; the most apparent one being the well studied nodal domain partition. An alternative partition is revealed by considering a set of…

Motivated by the definition of the smooth manifold structure on a suitable mapping space, we consider the general problem of how to transfer local properties from a smooth space to an associated mapping space. This leads to the notion of…

Almost contact manifolds with B-metric are considered. A special linear connection is introduced, which preserves the almost contact B-metric structure on these manifolds. This connection is investigated on some classes of the considered…

We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…

This paper explores the relationship that exists between nonlinear normal modes (NNMs) defined as invariant manifolds in phase space and the spectral expansion of the Koopman operator. Specifically, we demonstrate that NNMs correspond to…

We lay down an elementary yet fundamental lemma concerning a finite algebraicness property of a smooth map from an Azumaya/matrix manifold with a fundamental module to a smooth manifold. This gives us a starting point to build a synthetic…

We study PL bordism theories from a quantitative perspective. Such theories include those of PL manifolds, ordinary homology theory, as well as various more exotic theories such as bordism of Witt spaces. In all these cases we show that a…

Almost contact manifolds with B-metric are considered. Of special interest are the so-called vertical classes of the almost contact B-metric manifolds. Curvature properties of these manifolds are studied. An example of 5-dimensional…

A Universal Mapping Property is generally described as a characterization of an object up to a unique isomorphism by considering its relation to every other object; however, the term "by considering its relation to every other object" is…

We deduce continuity, compactness and invariance properties for quasi-Banach Orlicz modulation spaces. We characterize such spaces in terms of Gabor expansions and by their images under the Bargmann transform.

The aim of this paper is to give a new description of the geometry appearing in the multi-specialization along a general family of submanifolds of a real analytic manifold (including some important cases as clean intersection or a…

We study decay and compact support properties of positive and bounded solutions of $\Delta_{p} u \geq \Lambda(u)$ on the exterior of a compact set of a complete manifold with rotationally symmetry. In the same setting, we also give a new…

One of the main challenges in modern deep learning is to understand why such over-parameterized models perform so well when trained on finite data. A way to analyze this generalization concept is through the properties of the associated…

The nodal set of a Laplacian eigenfunction forms a partition of the underlying manifold or graph. Another natural partition is based on the gradient vector field of the eigenfunction (on a manifold) or on the extremal points of the…

A theorem of Mumford states that, on complex surfaces, any normal isolated singularity whose link is diffeomorphic to a sphere is actually a smooth point. While this property fails in higher dimensions, McLean asks whether the contact…

Lipschitz continuity of the gradient mapping of a continuously differentiable function plays a crucial role in designing various optimization algorithms. However, many functions arising in practical applications such as low rank matrix…

In this work, we derive some novel properties of the bimodal normal distribution. Some of its mathematical properties are examined. We provide a formal proof for the bimodality and assess identifiability. We then discuss the maximum…