Riemann's work on minimal surfaces
pp. 135-150
in: Lizhen Ji, Athanase Papadopoulos, Sumio Yamada (eds), From Riemann to differential geometry and relativity, Berlin, Springer, 2017Abstract
Three months before his death in 1866, Riemann left a set of notes to K. Hattendorff, a disciple of his, on minimal surfaces with boundary. Afterwards, Hattendorff supplied the text to the notes mostly consisting of computations, which became the two papers on the subject: "On the surface of least area with a given boundary" and "Examples of surfaces of least area with a given boundary." We will go over the expositions and provide an overview from the modern viewpoint, make some comments on Riemann-Hattendorff's text, and compare the work with that of Weierstrass on the same subject.