A theorem of Hopf and the Cauchy-Riemann inequality

Hilario Alencar (), Manfredo do Carmo () and Renato Tribuzy ()
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Hilario Alencar: Universidade Federal de Alagoas, Departamento de Matemática
Manfredo do Carmo: Universidade Federal de Alagoas, Departamento de Matemática
Renato Tribuzy: Universidade Federal de Alagoas, Departamento de Matemática

A chapter in Manfredo P. do Carmo – Selected Papers, 2012, pp 441-456 from Springer

Abstract: Abstract In 1951, Hopf [9] published a theorem in a seminal paper on surfaces of constant mean curvature which can be stated as follows. Let a genus zero compact surface M be immersed in $${\mathbb{R}^3}$$ with constant mean curvature H. Then M is isometric to the standard sphere. Hopf gave two proofs of this result (see [9] for details).

Keywords: Quadratic Form; Neighborhood Versus; Ambient Space; Curvature Vector; Compact Surface (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-25588-5_32

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DOI: 10.1007/978-3-642-25588-5_32

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