7 citations · 22 across the 16 of their papers we have counts for
17 papers
Extreme non-differentiability of typical Lipschitz mappings
Michael Dymond, Olga Maleva
We show that no matter what subset of a normed space is given, a typical 1-Lipschitz mapping into a Banach space is non-differentiable at a typical point of the set in a very stron…
On extremal nonexpansive mappings
Christian Bargetz, Michael Dymond, Katriin Pirk
We study the extremality of nonexpansive mappings on a nonempty bounded closed and convex subset of a normed space (therein specific Banach spaces). We show that surjective isometr…
Typical Lipschitz mappings are typically non-differentiable
Michael Dymond, Olga Maleva
We prove that a typical Lipschitz mapping between any two Banach spaces is non-differentiable at typical points of any given subset of its domain in the most extreme form. This is…
Porosity phenomena of non-expansive, Banach space mappings
Michael Dymond
For any non-trivial convex and bounded subset of a Banach space, we show that outside of a -porous subset of the space of non-expansive mappings , all mappings have…
Divergence of separated nets with respect to displacement equivalence
Michael Dymond, Vojtěch Kaluža
We introduce a hierachy of equivalence relations on the set of separated nets of a given Euclidean space, indexed by concave increasing functions .…
Lipschitz constant almost surely suffices for mapping grid points onto a cube
Michael Dymond
Kaluža, Kopecká and the author have shown that the best Lipschitz constant for mappings taking a given -element set in the integer lattice , with $n\in \math…
On the existence of fixed points for typical nonexpansive mappings on spaces with positive curvature
Christian Bargetz, Michael Dymond, Emir Medjic +1
We show that the typical nonexpansive mapping on a small enough subset of a CAT()-space is a contraction in the sense of Rakotch. By typical we mean that the set of nonexpansive…
A dichotomy of sets via typical differentiability
Michael Dymond, Olga Maleva
We obtain a criterion for an analytic subset of a Euclidean space to contain points of differentiability of a typical Lipschitz function, namely, that it cannot be covered by count…
Highly irregular separated nets
Michael Dymond, Vojtěch Kaluža
In 1998 Burago and Kleiner and (independently) McMullen gave examples of separated nets in Euclidean space which are non-bilipschitz equivalent to the integer lattice. We study wea…
Typical differentiability within an exceptionally small set
Michael Dymond
We verify the existence of a purely unrectifiable set in which the typical Lipschitz function has a large set of full differentiability points. The example arises from a constructi…
Mapping grid points onto a square forces an arbitrarily large Lipschitz constant
Michael Dymond, Vojtěch Kaluža, Eva Kopecká
We prove that the regular square grid of points in the integer lattice cannot be recovered from an arbitrary -element subset of …
On the structure of universal differentiability sets
Michael Dymond
We prove that universal differentiability sets in Euclidean spaces possess distinctive structural properties. Namely, we show that any universal differentiability set contains a `k…
Porosity Results for Sets of Strict Contractions on Geodesic Metric Spaces
Christian Bargetz, Michael Dymond, Simeon Reich
We consider a large class of geodesic metric spaces, including Banach spaces, hyperbolic spaces and geodesic -spaces, and investigate the space of nonexpansive map…
σ-Porosity of the set of strict contractions in a space of non-expansive mappings
Christian Bargetz, Michael Dymond
We consider the space of non-expansive mappings on a bounded, closed and convex subset of a Banach space equipped with the metric of uni- form convergence. We show that the set of…
Avoiding σ-porous sets in Hilbert spaces
Michael Dymond
We give a constructive proof that any -porous subset of a Hilbert space has Lebesgue measure zero on typical curves. Further, we discover that this result does not exten…
On interval based generalizations of absolute continuity for functions on
Michael Dymond, Beata Randrianantoanina, Huaqiang Xu
We study notions of absolute continuity for functions defined on similar to the notion of -absolute continuity in the sense of Bongiorno. We confirm a conjecture o…
Differentiability inside sets with upper Minkowski dimension one
Michael Dymond, Olga Maleva
We show that every finite-dimensional Euclidean space contains compact universal differentiability sets of upper Minkowski dimension one. In other words, there are compact sets …