Let F = Fg,n be a surface of genus g with n punctures. We assume 3g − 3 + n > 1 and that (g, n) 6= (1, 2). The purpose of this paper is to prove, for the Weil-Petersson metric on Teichmuller space Tg,n, the analogue of Royden’s famous result [15] that every complex analytic isometry of Tg,0 with respect to the Teichmuller metric is induced by an element of the mapping class group. His proof inv...

Coxeter classified all discrete isometry groups generated by reflections that act on a Euclidean space or on a sphere of an arbitrary dimension (see [1]). His fundamental work became classical long ago. Lobachevsky spaces (classical hyperbolic spaces) are as symmetric as Euclidean spaces and spheres. However, discrete isometry groups generated by reflections, with fundamental polytopes of finit...

For some finite set A of points in R n and some integer k ∈ N we consider the problem of reconstructing the set A up to isometry from the multiset of the |A| k subsets of A of cardinality k given up to isometry. We prove the best possible result for n = 1 and settle an open problem for n = 2 mentioned by Krasikov and Roditty in [8].

Due to the nature of multiplicative Rayleigh fading, symmetric space time block codes, and joint estimation and detection schemes, isometry (ambiguities in channel estimation and data detection) degrades MIMO system performances. Training breaks isometry but reduces capacity. Asymmetric space time block code mitigates isometry by replacing training with data-bearing asymmetric codewords. This p...

Let M(n) denote the group of orientation-preserving isometries of H. Classically, one uses the disk model for H to define the dynamical type of an isometry. In this model an isometry is elliptic if it has a fixed point on the disk. An isometry is parabolic, resp. hyperbolic, if it is not elliptic and has one, resp. two fixed points on the conformal boundary of the hyperbolic space. If in additi...

We show that a finite metric space A admits an extension to a finite metric space B so that each partial isometry of A extends to an isometry of B. We also prove a more precise result on extending a single partial isometry of a finite metric space. Both these results have consequences for the structure of the isometry groups of the rational Urysohn metric space and the Urysohn metric space.

In this paper we look at isometry properties of random matrices. During the last decade these properties gained a lot attention in a field called compressed sensing in first place due to their initial use in [7, 8]. Namely, in [7, 8] these quantities were used as a critical tool in providing a rigorous analysis of l1 optimization’s ability to solve an under-determined system of linear equations...

The aim of this paper is to lay the groundwork for a theory of quadratic forms over several significant, and quite extensive, classes of preordered rings. By “quadratic forms” we understand, here, diagonal quadratic forms with unit coefficients; and “ring” stands for commutative unitary ring where 2 in invertible. We achieve this by the use, in the ring context, of our abstract theory of quadra...

We obtain infinite classes of new Einstein-Sasaki metrics on complete and nonsingular manifolds. They arise, after Euclideanization, from BPS limits of the rotating Kerr-de Sitter black hole metrics. The new Einstein-Sasaki spaces L(p,q,r) in five dimensions have cohomogeneity 2 and U(1) x U(1) x U(1) isometry group. They are topologically S(2) x S(3). Their AdS/CFT duals describe quiver theori...