Tohoku Mathematical Journal

Deformation and stability of surfaces with constant mean curvature

Miyuki Koiso

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For a CMC immersion from a two-dimensional compact smooth manifold with boundary into the Euclidean three-space, we give sufficient conditions under which it has a CMC deformation fixing the boundary. Moreover, we give a criterion of the stability for CMC immersions. Both of these are achieved by using the properties of eigenvalues and eigenfunctions of an eigenvalue problem associated to the second variation of the area functional. In a certain special case, by combining these results, we obtain a 'visible' way of judging the stability.

Article information

Tohoku Math. J. (2), Volume 54, Number 1 (2002), 145-159.

First available in Project Euclid: 11 April 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58E12: Applications to minimal surfaces (problems in two independent variables) [See also 49Q05]
Secondary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]


Koiso, Miyuki. Deformation and stability of surfaces with constant mean curvature. Tohoku Math. J. (2) 54 (2002), no. 1, 145--159. doi:10.2748/tmj/1113247184.

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