Memoirs of the American Mathematical Society 2011; 79 pp; softcover Volume: 211 ISBN10: 082184914X ISBN13: 9780821849149 List Price: US$66 Individual Members: US$39.60 Institutional Members: US$52.80 Order Code: MEMO/211/991
 In this memoir the authors revisit Almgren's theory of \(Q\)valued functions, which are functions taking values in the space \(\mathcal{A}_Q(\mathbb{R}^{n})\) of unordered \(Q\)tuples of points in \(\mathbb{R}^{n}\). In particular, the authors:  give shorter versions of Almgren's proofs of the existence of \(\mathrm{Dir}\)minimizing \(Q\)valued functions, of their Hölder regularity, and of the dimension estimate of their singular set;
 propose an alternative, intrinsic approach to these results, not relying on Almgren's biLipschitz embedding \(\xi: \mathcal{A}_Q(\mathbb{R}^{n})\to\mathbb{R}^{N(Q,n)}\);
 improve upon the estimate of the singular set of planar \(\mathrm{D}\)minimizing functions by showing that it consists of isolated points.
Table of Contents  Introduction
 The elementary theory of \(Q\)valued functions
 Almgren's extrinsic theory
 Regularity theory
 Intrinsic theory
 The improved estimate of the singular set in \(2\) dimensions
 Bibliography
