| Résume | I will begin by reviewing classical geometric properties of
constant mean curvature surfaces, H>0, in R3. I will then talk about several
more recent results for surfaces embedded in R3 with constant mean curvature,
such as curvature and radius estimates.
I will show applications of such estimates including a characterisation of the
round sphere as the only simply-connected surface embedded in R 3 with
constant mean curvature and area estimates for compact surfaces embedded in a
flat torus with constant mean curvature and finite genus.
I will also talk about the geometry of compact hyper surfaces embedded in a
manifold with constant mean curvature and finite index. |
