Related papers: Sublinear biLipschitz equivalence and sublinearly …

Let $X$ be a proper geodesic metric space. We give a new construction of the Morse Boundary that realizes its points as equivalence classes of functions on $X$ which behave similar to the "distance to a point" function. When $G=\langle S…

The Reeb space of a smooth map whose codimension is minus is the space defined as the space of all connected components of inverse images. For generic maps such as Morse functions and their higher dimensional versions, they are polyhedra…

This article investigates the weak approximation towards the invariant measure of semi-linear stochastic differential equations (SDEs) under non-globally Lipschitz coefficients. For this purpose, we propose a linear-theta-projected Euler…

We give a proof of the sublinear tracking property for sample paths of random walks on various groups acting on spaces with hyperbolic-like properties. As an application, we prove sublinear tracking in Teichmueller distance for random walks…

The Reeb space of a generic map is the space of all connected components of preimages of the map. Reeb spaces are fundamental and useful tools in the theory of Morse functions and higher dimensional variants and their applications to…

We provide analogues of the results from [FMR11, CMMR13] in the reference list (which correspond to the case $\kappa = \omega$) for arbitrary $\kappa$-Souslin quasi-orders on any Polish space, for $\kappa$ an infinite cardinal smaller than…

We study the structure of the space of coarse Lipschitz maps between Banach spaces. In particular we introduce the notion of norm attaining coarse Lipschitz maps. We extend to the case of norm attaining coarse Lipschitz equivalences, a…

This article analyzes sublinearly quasisymmetric homeo-morphisms (generalized quasisymmetric mappings), and draws applications to the sublinear large-scale geometry of negatively curved groups and spaces. It is proven that those…

Suppose that $E$ and $E'$ denote real Banach spaces with dimension at least 2 and that $D\varsubsetneq E$ and $D'\varsubsetneq E'$ are uniform domains with homogeneously dense boundaries. We consider the class of all $\varphi$-FQC (freely…

We prove a complete characterization of the extremal invariant measures for half-space geometric last-passage percolation with an arbitrary boundary parameter. This is the first result of its kind for a model in the KPZ universality class…

The article is devoted to a proof of the optimal upper-bound for Morse Lemma, its "anti"-version and their applications. Roughly speaking, Morse Lemma states that in a hyperbolic metric space, a $\lambda$-quasi-geodesic $\gamma$ sits in a…

The aim of this paper is to investigate the class of quasi $\kappa$-metrizable spaces. This class is invariant with respect to arbitrary products and contains Shchepin's $\kappa$-metrizable spaces as a proper subclass.

Let $\Omega\subset \mathbb{R}^n$ be non-empty, open and proper. Consider $Wb(\Omega)$, the space of finite Borel measures on $\Omega$ equipped with the partial transportation metric introduced by Figalli and Gigli that allows the creation…

We show that the outside equation of a bounded elliptically symmetric lens (ESL) exhibits a pseudo-caustic that arises from a branch cut. A pseudo-caustic is a curve in the source plane across which the number of images changes by one. The…

We show that for some negatively curved solvable Lie groups, all self quasiisometries are almost isometries. We prove this by showing that all self quasisymmetric maps of the ideal boundary (of the solvable Lie groups) are bilipschitz with…

We initiate the study of the small scale geometry of operator spaces. The authors have previously shown that a map between operator spaces which is completely coarse (that is, the sequence of its amplifications is equi-coarse) must be…

We define a notion of a rotund quasi-uniform space and describe a new direct construction of a (right-continuous) quasi-pseudometric on a (rotund) quasi-uniform space. This new construction allows to give alternative proofs of several…

Let $Y\subseteq \mathbb{R}^n$ be a closed definable subset and $X\subseteq \mathbb{R}^n$ be a smooth manifold. We construct a version of Morse theory for the restriction to $X$ of the Euclidean distance function from $Y$. This is done using…

We give sufficient conditions for a metric space to bilipschitz embed in L_1. In particular, if X is a length space and there is a Lipschitz map u:X--->R such that for every interval I in R, the connected components of the inverse image…

We consider a large class of geodesic metric spaces, including Banach spaces, hyperbolic spaces and geodesic $\mathrm{CAT}(\kappa)$-spaces, and investigate the space of nonexpansive mappings on either a convex or a star-shaped subset in…