Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 54, Number 1 (2002), 145-159.
Deformation and stability of surfaces with constant mean curvature
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.
Tohoku Math. J. (2), Volume 54, Number 1 (2002), 145-159.
First available in Project Euclid: 11 April 2005
Permanent link to this document
Digital Object Identifier
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. https://projecteuclid.org/euclid.tmj/1113247184