Stability of a constant mean curvature surface in R3

Publisher: Cambridge University Press

E-ISSN: 1755-1633|36|1|19-24

ISSN: 0004-9727

Source: Bulletin of the Australian Mathematical Society, Vol.36, Iss.1, 1987-08, pp. : 19-24

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

We solve the question raised by Barbosa and do Carmo as to whether there exists a complete, noncompact stably immersed surface in R3 with nonzero constant mean curvature. We show that such a surface is necessarily minimal, that is, its mean curvature is zero.