Related papers: Distances between surfaces in 4-manifolds

The aim of this paper is to extend some basic results about marginally outer trapped surfaces to the context of surfaces having general null expansion. Motivated in part by recent work of Chai-Wan, we introduce the notion of…

We prove a stability theorem for spaces of smooth concordance embeddings. From it we derive various applications to spaces of concordance diffeomorphisms and homeomorphisms.

Motivated by the embedding problem of canonical models in small codimension, we extend Severi's double point formula to the case of surfaces with rational double points, and we give more general double point formulae for varieties with…

We introduce an asymmetric distance function, which we call the `left Hausdorff distance function', on the space of geodesic laminations on a closed hyperbolic surface of genus at least 2. This distance is an asymmetric version of the…

Let $M$ be a smooth, orientable, closed, connected $4$-manifold and suppose that $H_1(M;\mathbb{Z})$ is finitely generated and has no $2$-torsion. We give a homotopy decomposition of the suspension of $M$ in terms of spheres, Moore spaces…

We prove that for every natural number k there are simply connected topological four-manifolds which have at leat k distinct smooth structures supporting Einstein metrics, and also have infinitely many distinct smooth structures not…

The natural occurrence of singular spaces in applications has led to recent investigations on performing topological data analysis (TDA) in a stratified framework. In many applications, there is no a priori information on what points should…

Here we study two interesting smooth contractible manifolds, whose boundaries have non-trivial mapping class groups. The first one is a non-Stein contractible manifold, such that every self diffeomorphism of its boundary extends inside;…

In this note, we combine the recent 4-dimensional light bulb theorem of David Gabai and a recent construction of concordances for knots in $S^2\times S^1$ due to Eylem Zeliha Yildiz to construct a concordance between the standard surface of…

In this paper we prove two theorems. The first one is a structure result that describes the extrinsic geometry of an embedded surface with constant mean curvature (possibly zero) in a homogeneously regular Riemannian three-manifold, in any…

Einstein equations are addressed with the energy-momentum tensor that appears if the equations under discussion are required to possess conformal invariance. It is proved that thus derived equations (equations of conformally invariant…

Consider a set of $n$ data points in the Euclidean space $\mathbb{R}^d$. This set is called dataset in machine learning and data science. Manifold hypothesis states that the dataset lies on a low-dimensional submanifold with high…

In this article, we define the contact surgery distance of two contact 3-manifolds $(M,\xi)$ and $(M',\xi')$ as the minimal number of contact surgeries needed to obtain $(M,\xi)$ from $(M',\xi')$. Our main result states that the contact…

In theories with extra dimensions the Standard Model Higgs field can be identified with the internal components of higher-dimensional gauge fields (Higgs-gauge unification). The higher-dimensional gauge symmetry prevents the Higgs mass from…

Let $M$ be a closed Riemannian manifold and let $X\subseteq M$. If the sample $X$ is sufficiently dense relative to the curvature of $M$, then the Gromov-Hausdorff distance between $X$ and $M$ is bounded from below by half their Hausdorff…

Let $M$ be a closed, oriented, simply connected 6-manifold. After localization away from 2, we give a homotopy decomposition of $\Sigma M$ in terms of spheres, Moore spaces and other recognizable spaces. As applications we calculate…

One of the primary methods of studying the topology of configurations of points in a graph and configurations of disks in a planar region has been to examine discrete combinatorial models arising from the underlying spaces. Despite the…

We study $\lambda$-hypersurfaces that are critical points of a Gaussian weighted area functional $\int_{\Sigma} e^{-\frac{|x|^2}{4}}dA$ for compact variations that preserve weighted volume. First, we prove various gap and rigidity theorems…

We study the properties of sets $\Sigma$ which are the solutions of the maximal distance minimizer problem, id est of sets having the minimal length (one-dimensional Hausdorff measure) over the class of closed connected sets $\Sigma \subset…

We show that any closed oriented 3-manifold can be topologically embedded in some simply-connected closed symplectic 4-manifold, and that it can be made a smooth embedding after one stabilization. As a corollary of the proof we show that…