Connections between the three areas have been recognized for several decades now, and mathematicians have progressively realized that the study of them requires taking into account certain important geometric structures associated with the underlying metric and measure in high-dimensional and infinite-dimensional spaces. Contributors here take the task on, with papers on such aspects as the maximal characterization of Hardy-Sobolev spaces on manifolds, approximately Gaussian marginals and the hyperplane conjecture, on the existence of sub-Gaussian directions for log-concave measures, isoperimetric bounds on convex manifolds, and the log-convex density conjecture. There is no index. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)