On Almgren's regularity result (Q1568985)

The author gives a brief summary of the most important aspects of the late Frederick Almgren's proof that the singularities of an area-minimizing integral current are of at least codimension two in the current. More precisely, Almgren proved that if the area-minimizing current is \(m\)-dimensional, \(S\) denotes the singular set, and \(\varepsilon >0\) is arbitrary, then \(H^{m-2+\varepsilon}(S) = 0,\) where \(H^{m-2+\varepsilon}\) denotes the \((m-2+\varepsilon)\)-dimensional Hausdorff measure. Almgren's original preprint was over 1700 pages long, so clearly the paper under review can, and does, only provide an outline of Almgren's work.