Riemann’s Work on Minimal Surfaces

Sumio Yamada ()
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Sumio Yamada: Gakushuin University, Department of Mathematics

A chapter in From Riemann to Differential Geometry and Relativity, 2017, pp 135-150 from Springer

Abstract: Abstract 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.

Keywords: Riemann; Minimal surface; Calculus of variations; 53A10; 30F45 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-60039-0_5

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DOI: 10.1007/978-3-319-60039-0_5

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