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(2017) From Riemann to differential geometry and relativity, Dordrecht, Springer.
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.
Publication details
DOI: 10.1007/978-3-319-60039-0_5
Full citation:
Yamada, S. (2017)., Riemann's work on minimal surfaces, in L. Ji, A. Papadopoulos & S. Yamada (eds.), From Riemann to differential geometry and relativity, Dordrecht, Springer, pp. 135-150.
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