TY - JOUR
T1 - Deformation and stability of surfaces with constant mean curvature
AU - Koiso, Miyuki
PY - 2002
Y1 - 2002
N2 - 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.
AB - 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.
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U2 - 10.2748/tmj/1113247184
DO - 10.2748/tmj/1113247184
M3 - Article
AN - SCOPUS:0036492253
VL - 54
SP - 145
EP - 159
JO - Tohoku Mathematical Journal
JF - Tohoku Mathematical Journal
SN - 0040-8735
IS - 1
ER -