We determine the number of cusps of minimal Picard modular surfaces. The proof also counts cusps of other Picard modular surfaces of arithmetic interest. Consequently, for each N > 0 there are finitely many commensurability classes of nonuniform arithmetic lattices in SU(2, 1) that contain an N -cusped surface. We also discuss a higher-rank analogue.

There are three main observations which make up the proof. The first observation, discussed in Section 2, is that convex co-compact subgroups of a fundamental group of a hyperbolic 3-manifold N persist in the approximates given by hyperbolic Dehn surgery. This result is stated formally as Proposition 2.1. The second observation, discussed in Section 4, is that a collection of distinct hyperboli...

In this paper we count the number of cusps of minimal non-compact finite volume arithmetic hyperbolic 3-orbifolds. We show that for each N , the orbifolds of this kind which have exactly N cusps lie in a finite set of commensurability classes, but either an empty or an infinite number of isometry classes.

In this article, we prove that the commensurability class of a closed, orientable, hyperbolic 3–manifold is determined by the surface subgroups of its fundamental group. Moreover, we prove that there can be only finitely many closed, orientable, hyperbolic 3–manifolds that have the same set of surfaces.

© 1995-2012 IEEE. We present the first reliability study of InAs/GaAs self-assembled quantum dot lasers epitaxially grown on Ge/Si substrates. Some devices maintain lasing oscillation after more than 2700 h of constant current stress at 30 °C, longer than any previous life tests of GaAs lasers epitaxially grown on silicon. No catastrophic failures were observed. The lasers were characterized to...

(1) Background: Is variation among the communities of a metacommunity higher than within communities? Community ecologists and population geneticists often characterize structure metacommunities by partitioning (diversity) into two following components using measures such as FST or GST α- β-diversity. The within-communities component is usually some average (type, species, genetic) diversities ...

The “emotion curve” is a creative methodology that asks research participants to express in graphic form changes their emotional responses over time, reflecting on given time period or particular activity event (in our case, music-based activities). This was developed as part of with community music-making NGO Musicians Without Borders at “Music Bridge” participatory music and movement training...