Tohoku Mathematical Journal
2002
March
SECOND SERIES VOL. 54, NO. 1

Tohoku Math. J.
54 (2002), 145-159

Title DEFORMATION AND STABILITY OF SURFACES WITH CONSTANT MEAN CURVATURE

Author Miyuki Koiso

(Received April 26, 2000, revised February 13, 2001)
Abstract. 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.

2000 Mathematics Subject Classification. Primary 58E12; Secondary 53C42, 53A10.

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