Integral criteria for closed surfaces with constant mean curvature
2007 ◽
Vol 463
(2081)
◽
pp. 1199-1210
Keyword(s):
We propose three integral criteria that must be satisfied by all closed surfaces with constant mean curvature immersed in the three-dimensional Euclidean space. These criteria are integral identities that follow from requiring the second variation of the area functional to be invariant under rigid displacements. We obtain from them a new proof of the old result by Delaunay, to the effect that the sphere is the only closed axis-symmetric surface.
1995 ◽
Vol 10
(03)
◽
pp. 337-364
◽
1989 ◽
pp. 91-94
1991 ◽
Vol 147
(2)
◽
pp. 375-379
◽
Keyword(s):
2003 ◽
Vol 83
(4)
◽
pp. 281-293
◽
1988 ◽
Vol s2-38
(2)
◽
pp. 333-340