We prove the plasticity of unit ball c. That is, we show that every non-expansive bijection from c onto itself is an isometry. also demonstrate a slightly weaker property for c0 – isometry, provided it has continuous inverse.

We consider the equivalence relation of isometry of separable, complete metric spaces, and show that any equivalence relation induced by a Borel action of a Polish group on a Polish space is Borel reducible to this isometry relation. We also consider the isometry relation restricted to various classes of metric spaces, and produce lower bounds for the complexity in terms of the Borel reducibili...

Every isometry of a finite dimensional euclidean space is a product of reflections and the minimum length of a reflection factorization defines a metric on its full isometry group. In this article we identify the structure of intervals in this metric space by constructing, for each isometry, an explicit combinatorial model encoding all of its minimal length reflection factorizations. The model ...

It was pointed out by Couch and Torrence that the extreme Reissner-Nordström solution possesses a discrete conformal isometry. Using results of Romans, it is shown that such a symmetry also exists when a non-zero cosmological constant is allowed. Introduction In [1], Couch and Torrence found a conformal isometry that interchanges the event horizon and null infinity J of an extremal Reissner-Nor...

It is shown that for many finite dimensional normed vector spaces V over C, a linear projection P : V → V will have nice structure if P + λ(I − P ) is an isometry for some complex unit not equal to one. From these results, one can readily determine the structure of bicircular projections, i.e., those linear projections P such that P + μ(I − P ) is a an isometry for every complex unit μ. The key...

We address the problem of correspondence between 3D isometric shapes. We present an automatic method that finds the optimal correspondence between two given (nearly) isometric shapes by minimizing the amount of deviation from isometry. We optimize the isometry error in two steps. In the first step, the 3D points uniformly sampled from the shape surfaces are transformed into spectral domain base...