On Intrinsic Isometries to Euclidean Space

Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings

for all x ∈ X . Quasi-isometries occur naturally in the study of the geometry of discrete groups since the length spaces on which a given finitely generated group acts cocompactly and properly discontinuously by isometries are quasi-isometric to one another [Gro]. Quasi-isometries also play a crucial role in Mostow’s proof of his rigidity theorem: the theorem is proved by showing that equivaria...

A Note on Coincidence Isometries of Modules in Euclidean Space

It is shown that the coincidence isometries of certain modules in Euclidean n-space can be decomposed into a product of at most n coincidence reflections defined by their non-zero elements. This generalizes previous results obtained for lattices to situations that are relevant in quasicrystallography.

Coulomb Shapes: Using Electrostatic Forces for Deformation-invariant Shape Representation

Canonical shape analysis is a popular method in deformable shape matching, trying to bring the shape into a canonical form that undoes its non-rigid deformations, thus reducing the problem of non-rigid matching into a rigid one. The canonization can be performed by measuring geodesic distances between all pairs of points on the shape and embedding them into a Euclidean space by means of multidi...

Metric Rigidity of Crystallographic Groups

Consider a finite set of Euclidean motions and ask what kind of conditions are necessary for this set to generate a crystallographic group. We investigate a set of Euclidean motions together with a special concept motivated by real crystalline structures existing in nature, called an essential crystallographic set of isometries. An essential crystallographic set of isometries can be endowed wit...

On images of continuous functions from a compact manifold to Euclidean space