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.

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.

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...

Since the early 1970s, mathematicians have tried to extend the work of N. Fenichel and M. Hirsch, C. Pugh and M. Shub, to give conditions under which invariant manifolds for semi-flows persist under perturbation of the semiflow. This work provides natural conditions and establishes the desired theorem. The technique is geometric in nature, and in addition to rigorous proofs, an informal outline of the approach is given with useful illustrations.

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

The equivalence relation of concordance on the set of links of circles in 3-space arises naturally in attempts to resolve singularities of immersed 2-spheres in a 4-dimensional manifold. In fact, certain unsolved link concordance problems are exactly the obstructions to successfully performing surgery on 4-manifolds as the higher-dimensional theory predicts.

Let $mathcal S$ be a second order smoothness in the $mathbb DEGREESn$ setting. We can assume without loss of generality that the dimension $n$ has been adjusted as necessary so as to insure that $mathcal S$ is also non-degenerate. This title describes how $mathcal S$ must fit into one of three mutually exclusive cases, and in each of these cases the authors characterize, by a simple intrinsic condition, the second order smoothnesses $mathcal S$ whose canonical Sobolev projection $P_$ is of weak type $(1,1)$ in the $mathbb DEGR

The Second Chinburg Conjecture relates the Galois module structure of rings of integers in number fields to the values of the Artin root number on the symplectic representations of the Galois group. This book establishes the Second Chinburg Conjecture for various quaternion fields.

This paper is concerned with the computational estimation of the error of numerical solutions of potentially degenerate reaction-diffusion equations. The underlying motivation is a desire to compute accurate estimates as opposed to deriving inaccurate analytic upper bounds. The authors outline, analyze and test an approach to obtain computational error estimates based on the introduction of the residual error of the numerical solution and in which the effects of the accumulation of errors are estimated computationally.