This book is intended for graduate students and research mathematicians interested in set theory.

The authors employ advances in the theory of operator spaces, also known as quantized functional analysis, to provide a context in which one can compare categories of modules over operator algebras that are not necessarily self-adjoint. Attention is focused on the category of Hilbert modules over an operator algebra and on the category of operator modules over an operator algebra. The module operations are assumed to be completely bounded - usually, completely contractive.

This work is devoted to the case of constant mean curvature surfaces immersed in R (or, more generally, in spaces of constant curvature). Wente reduces this geometrical problem to finding certain integrable solutions to the Gauss equation. Many new and interesting examples are presented, including immersed cylinders in R with embedded Delaunay ends and n-lobes in the middle, and one-parameter families of immersed cmc tori in R . Finally, Wente examines minimal surfaces in hyperbolic three-space, which is in some ways the most complicated case.

In 1940, A A Lyapunov published his celebrated discovery that the range of a nonatomic vector-valued measure is convex and compact. This book presents the result of a systematic generalization of Lyapunov's theorem to the setting of operator algebras. The author's point of view follows that of Lindenstrauss, so that, in their terminology, Lyapunov's theorem asserts that if *v is a weak* continuous map of a nonatomic abelian von Neumann algebra *N into Cn, and B denotes the positive part of the unit ball of *N, then for each a *e B there is an extreme point p of B (i.e., a projection) with *v...

Presents a systematic algorithm for proving that certain cones are area-minimizing. The algorithm the author describes consists of examining a first order ordinary equation based on the curvature and dimension of the cone and ensuring that certain line segments normal to the curve do not intersect.

This work investigates analytic torsion on the moduli space of degree zero stable bundles on a compact Reimann surface. Zeta-function regularization and perturbation-curvature formulas for torsion are developed using a modified resolvent-Szego kernel. The author discusses the bosonization formulas of mathematical physics. Riemann vanishing theorems for torsion, and analytic properties (insertion-residue formulas and heat equations) for the nonabelian theta function and Szego kernel. In addition, he provides background material on bundle-moduli spaces, Quillen metrics, and theta functions.

Using the theory of categories as a framework, this book develops a duality theory for theories in first order logic in which the dual of a theory is the category of its models with suitable additional structure. This duality theory resembles and generalizes M. H. Stone's famous duality theory for Boolean algebras. As an application, the author derives a result akin to the well-known definability theorem of E. W. Beth. This new definability theorem is related to theorems of descent in category theory and algebra and can also be stated as a result in pure logic without reference to category...

The nine finite, planar, 3-connected, edge-transitive graphs have been known and studied for many centuries. The infinite, locally finite, planar, 3-connected, edge-transitive graphs can be classified according to the number of their ends (the supremum of the number of infinite components when a finite subgraph is deleted). Prior to this study the 1-ended graphs in this class were identified by Grunbaum and Shephard as 1-skeletons of tessellations of the hyperbolic plane; Watkins characterized the 2-ended members. Any remaining graphs in this class must have uncountably many ends. In this...

Discusses duality theory of operator spaces (as developed by Effros-Ruan and Blecher-Paulsen) bounded operators are replaced by completely bounded ones, isomorphisms by complete isomorphisms, and Banach spaces by operator spaces. This book presents self du