THE GEOMETRY OF CONSTANT MEAN CURVATURE SURFACES IN EUCLIDEAN SPACE - GIUSEPPE TINAGLIA (KING'S COLLEGE LONDON)

I will begin by reviewing classical geometric properties of constant mean curvature surfaces, H>0, in R^3. I will then talk about several more recent results for surfaces embedded in R^3 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.

Please, contact the organisers (dgseminar.torino@gmail.com) in order to get the Webex link to participate.