Related papers: Contact equations, Lipschitz extensions and isoper…

M. Gromov introduced the Lipschitz order relation on the set of metric measure spaces and developed a rich theory. In particular, he claimed that an isoperimetric inequality on a non-discrete space is represented by using the Lipschitz…

This note is concerned with the geometric classification of connected Lie groups of dimension three or less, endowed with left-invariant Riemannian metrics. On the one hand, assembling results from the literature, we give a review of the…

We give some new methods, based on Lipschitz extension theorems, for bounding filling invariants of subsets of nonpositively curved spaces. We apply our methods to find sharp bounds on higher-order Dehn functions of Sol_{2n+1}, horospheres…

Main results of the paper: (1) For any finite metric space $M$ the Lipschitz free space on $M$ contains a large well-complemented subspace which is close to $\ell_1^n$. (2) Lipschitz free spaces on large classes of recursively defined…

The present paper is focused on the computation of the Lipschitz upper semicontinuity modulus of the feasible set mapping in the context of fully perturbed linear inequality systems; i.e., where all coefficients are allowed to be perturbed.…

We give a new CR invariant treatment of the bigraded Rumin complex and related cohomology groups via differential forms. A key benefit is the identification of balanced $A_\infty$-structures on the Rumin and bigraded Rumin complexes. We…

In this paper we study Lipschitz regularity of elliptic PDEs on geometric graphs, constructed from random data points. The data points are sampled from a distribution supported on a smooth manifold. The family of equations that we study…

We study a new bi-Lipschitz invariant \lambda(M) of a metric space M; its finiteness means that Lipschitz functions on an arbitrary subset of M can be linearly extended to functions on M whose Lipschitz constants are enlarged by a factor…

For each left-invariant semi-Riemannian metric $g$ on a Lie group $G$, we introduce the class of bi-Lipschitz Riemannian Clairaut metrics, whose completeness implies the completeness of $g$. When the adjoint representation of $G$ satisfies…

Almost paracontact Riemannian manifolds of the lowest dimension are studied, whose paracontact distributions are equipped with an almost paracomplex structure. These manifolds are constructed as a product of a real line and a 2-dimensional…

Given a geodesic inside a simply-connected, complete, non-positively curved Riemannian (NPCR) manifold M, we get an associated geodesic inside the asymptotic cone Cone(M). Under mild hypotheses, we show that if the latter is contained…

We consider subsets $S$ of a metric space $M$ such that Lipschitz mappings defined on $S$ can be extended to Lipschitz mappings on $M$, and we show that the union of such subsets has the same property under appropriate geometric conditions.…

In the metric spaces, we give some equivalent condition of intrinsically Lipschitz maps introduce by Franchi, Serapioni and Serra Cassano in subRiemannian Carnot groups. Unlike what happens in the Carnot groups, in our context intrinsic…

This paper deals with the study of parameter dependence of extensions of Lipschitz mappings from the point of view of continuity. We show that if assuming appropriate curvature bounds for the spaces, the multivalued extension operators that…

We give a new approach to the infinitesimal structure of Lipschitz maps into L^1. As a first application, we give an alternative proof of the main theorem from an earlier paper, that the Heisenberg group does not admit a bi-Lipschitz…

We discuss the notion of sublinearly bilipschitz equivalences (SBE), which generalize quasi-isometries, allowing some additional terms that behave sublinearly with respect to the distance from the origin. Such maps were originally motivated…

We mainly investigate some properties of quasiconformal mappings between smooth 2-dimensional surfaces with boundary in the Euclidean space, satisfying certain partial differential equations (inequalities) concerning Laplacian, and in…

Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We consider the…

We investigate contact Lie groups having a left invariant Riemannian or pseudo-Riemannian metric with specific properties such as being bi-invariant, flat, negatively curved, Einstein, etc. We classify some of such contact Lie groups and…

Let $\Sigma$ be a hypersurface in an $n$-dimensional Riemannian manifold $M$, $n\geqslant 2$. We study the isometric extension problem for isometric immersions $f:\Sigma\to\mathbb R^n$, where $\mathbb R^n$ is equipped with the Euclidean…