Related papers: Typical Lipschitz mappings are typically non-diffe…

A subspace of a multipartite Hilbert space is called \textit{locally indistinguishable} if any orthogonal basis of this subspace cannot be perfectly distinguished by local operations and classical communication. Previously it was shown that…

We show that there are separated nets in the Euclidean plane which are not biLipschitz equivalent to the integer lattice. The argument is based on the construction of a continuous function which is not the Jacobian of a biLipschitz map.

We prove that Ahlfors 2-regular quasisymmetric images of the Euclidean plane are bi-Lipschitz images of the plane if and only if they are uniformly bi-Lipschitz homogeneous with respect to a group. We also prove that certain geodesic spaces…

We extend the recent result of G. Godefroy which concerns the existence of non-norm attaining Lipschitz maps in order to characterize the norm attainment toward vectors for Lipschitz maps in the general setting of underlying space. The main…

We construct intrinsic Lipschitz graphs in Carnot groups with the property that, at every point, there exist infinitely many different blow-up limits, none of which is a homogeneous subgroup. This provides counterexamples to a Rademacher…

We show that the existence of a strongly convex function with a Lipschitz derivative on a Banach space already implies that the space is isomorphic to a Hilbert space. Similarly, if both a function and its convex conjugate are $C^2$ then…

It is known by a result of Mendes and Sampaio that the Lipschitz normal embedding of a subanalytic germ is fully characterized by the Lipschitz normal embedding of its link. In this note, we show that the result still holds for definable…

We show in this paper that every bijective linear isometry between the continuous section spaces of two non-square Banach bundles gives rise to a Banach bundle isomorphism. This is to support our expectation that the geometric structure of…

We show that the super fixed point property for nonexpansive mappings and for asymptotically nonexpansive mappings in the intermediate sense are equivalent. As a consequence, we obtain fixed point theorems for asymptotically nonexpansive…

We give conditions for topological and bi-Lipschitz equivalences within a class of mixed singularities of Pham-Brieskorn type. As a consequence, we construct infinite families that are topologically trivial but have distinct bi-Lipschitz…

In this paper Hilbert spaces are characterized among Banach spaces in terms of transitivity with respect to nicely behaved subgroups of the isometry group. For example, the following result is typical here: If X is a real Banach space…

We prove that the path space of a differentiable manifold is diffeomorphic to a Fr\'echet space, endowing the path space with a linear structure. Furthermore, the base point preserving mapping space consisting of maps from a cube to a…

An invertible function is bi-Lipschitz if both the function and its inverse have bounded Lipschitz constants. Nowadays, most Normalizing Flows are bi-Lipschitz by design or by training to limit numerical errors (among other things). In this…

The main purpose of the paper is to prove the following results: Let $A$ be a locally finite metric space whose finite subsets admit uniformly bilipschitz embeddings into a Banach space $X$. Then $A$ admits a bilipschitz embedding into $X$.…

We study metric measure spaces that admit "thick" families of rectifiable curves or curve fragments, in the form of Alberti representations or curve families of positive modulus. We show that such spaces cannot be bi-Lipschitz embedded into…

We provide a simple proof for the Fenchel duality between strong convexity and Lipschitz continuous gradient. To this end, we first establish equivalent conditions of convexity for a general function that may not be differentiable. By…

We develop a systematic approach to the study of duality for ideals of Lipschitz maps from a metric space to a Banach space, inspired by the classical theory that relates ideals of operators and tensor norms for Banach spaces, by using the…

The Dirichlet-to-Neumann map associated to an elliptic partial differential equation becomes multivalued when the underlying Dirichlet problem is not uniquely solvable. The main objective of this paper is to present a systematic study of…

We obtain an optimal deviation from the mean upper bound \begin{equation} D(x)\=\sup_{f\in \F}\mu\{f-\E_{\mu} f\geq x\},\qquad\ \text{for}\ x\in\R\label{abstr} \end{equation} where $\F$ is the class of the integrable, Lipschitz functions on…

This article studies typical 1-Lipschitz images of $n$-rectifiable metric spaces $E$ into $\mathbb{R}^m$ for $m\geq n$. For example, if $E\subset \mathbb{R}^k$, we show that the Jacobian of such a typical 1-Lipschitz map equals 1…